Table of contents

The 2010 edition of the Spanish Relativity Meeting (ERE2010) took place in Granada from 6–10 September 2010, and was hosted by the Instituto de Astrofísica de Andalucía (IAA - CSIC). This event represented the 34th edition of Encuentros Relativistas Españoles (ERE), an international conference devoted to relativity and gravitation and organized every year by one of the Spanish groups working in this area. The particular scientific flavour of the 2010 edition was captured by the subtitle of the conference, 'Gravity as a Crossroad in Physics'.

Our underlying rationale was to present gravitational physics as a scientific 'locus' for the interaction between (separate) communities in physics. It is a remarkable property of gravity that its specific problems provide a framework that calls for the interchange of ideas, concepts and methodologies from very different communities. In this edition we aimed to reflect this interdisciplinary perspective in the scientific programme. Each day during the week was devoted to a particular 'dialogue' between two communities who share some of their ultimate goals, but differ in their conceptual background, methodology or technical approach. These 'dialogues' were envisaged as opportunities to compare alternative viewpoints, maintaining a focus on their complementary nature. This led to the organization of the week as follows:

Day 1: Fundamental vs Effective Approaches in Theoretical Gravity This day compared approaches to gravity that differ conceptually in their understanding of the nature of the basic physical degrees of freedom of the theory, namely confronting viewpoints supporting the fundamental status of such degrees of freedom with other research programs favouring some emergence mechanism. Gravitational analogues were also discussed on this day.

Day 2: Geometric vs Quantum Field/String Theory Approaches to Quantum Gravity This day was focused on quantum gravity. A particular emphasis was placed on the comparison between geometric approaches to the quantization of general relativity (e.g. loop quantum gravity in the context of the canonical program) and approaches leaning on or evolving from a (quantum) field theory treatment of gravity (e.g. string/M-theory).

Day 3: Theoretical Cosmology vs Physical Cosmology This day addressed the current challenges in cosmology from a double perspective. On the one hand, offering an analysis of the large scale picture of the universe emerging from the accumulated body of observational data and, on the other hand, assessing the theoretical attempts to explain such a picture putting a special emphasis on the role of gravity.

Day 4: Relativity vs Astrophysics This day was focused on astrophysical problems where general relativity plays a fundamental role. Challenges and difficulties encountered by relativists modelling specific astrophysical scenarios were disucssed as well as the problems found by astrophysicists needing general relativity as a key conceptual ingredient. Particular emphasis was placed on gravitational waves and compact objects.

Day 5: Mathematical Relativity vs Numerical Relativity This day discussed fundamental problems in general relativity, and more generally in gravity physics, where a close collaboration between relativists in the geometry/analysis community on the one hand, and relativists in the numerical community on the other hand, can prove to be particularly successful and insightful.

The contributions in this volume have been organized in two blocks, corresponding to plenary and parallel sessions during the conference. In both cases we have kept the chronological order of the presented talks. The only exception to this rule is the parallel session dedicated to the memory of the late S Brian Edgar, labeled as IV.A during the conference, which we have placed immediately after the plenary session contributions.

The result of the 'dialogue experience' at the conference was extremely satisfactory and gratifying. Scientific sessions were thrilled by tantalizing and inspiring discussions, often continued in long walks around the Cármenes of the old city. In this spirit, we wish to thank all of the participants of the ERE meeting for their enthusiasm and especially the contributors to these proceedings for their synthesis effort.

Granada, 25 July 2011

Víctor Aldaya, Carlos Barceló and José Luis Jaramillo

Corrigendum added 2 June 2015: We acknowledge the funding provided by the MICINN (Ref: FIS2009-08009), Consejería de Economía, Innovación, Ciencia y Empleo, Junta de Andalucía (Ref: IAC10-I-7369) and CSIC for the organization of this meeting.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

Several features of classical gravity, combined with the existence of Davies-Unruh temperature of horizons, support the following paradigm: Gravitational field equations in a wide class of theories, including Einstein's theory, should be viewed as describing the thermodynamic limit of the statistical mechanics of (as yet unknown) atoms of spacetime. I present the conceptual evidence for this emergent paradigm and discuss several facets of this approach.

Hořava gravity is a relatively recent (Jan 2009) idea in theoretical physics for trying to develop a quantum field theory of gravity. It is not a string theory, nor loop quantum gravity, but is instead a traditional quantum field theory that breaks Lorentz invariance at ultra-high (presumably trans-Planckian) energies, while retaining approximate Lorentz invariance at low and medium (sub-Planckian) energies. The challenge is to keep the Lorentz symmetry breaking controlled and small — small enough to be compatible with experiment. I will give a very general overview of what is going on in this field, paying particular attention to the disturbing role of the scalar graviton.

The purpose of this contribution is is to discuss black hole entropy in the loop quantum gravity framework. Special attention is paid to the description of the microscopic degrees of freedom responsible for the entropy, the statement of the combinatorial problems that must be solved in order to count them, and the behaviour of the entropy as a function of the horizon area. In particular I will review the derivation of the Bekenstein-Hawking law and its logarithmic corrections. I end with a comparison between the results derived within loop quantum gravity and the ones obtained by other approaches.

The behavior of the gravitating vacuum energy density in an expanding universe is discussed. A scenario is presented with a step-wise relaxation of the vacuum energy density. The vacuum energy density moves from plateau to plateau and follows, on average, the steadily decreasing matter energy density. The current plateau with a small positive value of the vacuum energy density (effective cosmological constant) may result from a still not equilibrated contribution of the light massive neutrinos to the quantum vacuum.

A general introduction is given to what can be predicated about quantum gravity once the lessons from the standard model of particle physics are taken into account. In particular, the effective lagrangian point of view is briefly commented upon.

New progress in loop gravity has lead to a simple model of a 'general-covariant quantum field theory'. I sum up the definition of the model in self-contained form, in terms accessible to those outside the subfield. I emphasize its formulation as a generalized topological quantum field theory with an infinite number of degrees of freedom, and its relation to lattice theory. I list the indications supporting the conjecture that the model is related to general relativity and UV finite.

Motivated by scenarios of quantum gravity, Planck-suppressed deviations from Lorentz invariance are expected at observable energies. Ultra-High-Energy Cosmic Rays, the most energetic particles ever observed in nature, yielded in the last two years strong constraints on deviations suppressed by O(E²/M²_Pl) and also, for the first time, on space-time foam, stringy inspired models of quantum gravity. We review the most important achievements and discuss future outlooks.

De Sitter spacetime plays an important role in cosmology: the geometry of most inflationary models is close to de Sitter spacetime and so will be the late-time behavior of the present universe with accelerated expansion. In linearized perturbation theory the metric fluctuations in a de Sitter cosmology describe very well the anisotropies of the microwave background and the observed large scale structure. Recently there has been some interest in the need to go beyond the linear approximation to include the effect of matter loops. This will allow testing perturbation theory in a de Sitter background, checking possible large back-reaction effects on the de Sitter geometry, and also eventually to discriminate between inflationary models that lead to similar results at tree level. Working in the framework of stochastic gravity, or equivalently in the large N expansion, one may derive the two-point correlations for the gravitational fluctuations incorporating the effects of matter loops. One may characterize the quantum gravitational fluctuations in a gauge invariant way by the two-point functions of the linearized Riemann tensor. This can be given in terms of the two-point linearized Einstein and Weyl tensors. Assuming minimally coupled scalar fields in a de Sitter invariant state, the two-point functions of the linearized Einstein tensor over the de Sitter background have been computed in terms of de Sitter invariant bi-tensors.

We review the status of three-dimensional "general massive gravity" (GMG) in its linearization about an anti-de Sitter (adS) vacuum, focusing on critical points in parameter space that yield generalizations of "chiral gravity". We then show how these results extend to = 1 super-GMG, expanded about a supersymmetric adS vacuum, and also to the most general 'curvature-squared' = 1 supergravity model.

Black holes are an apparently unavoidable prediction of classical General Relativity, at least if matter obeys the strong energy condition ρ + 3p ≥ 0. However quantum vacuum fluctuations generally violate this condition, as does the eq. of state of cosmological dark energy ρ = −p > 0. When quantum effects are considered, black holes lead to a number of thermodynamic paradoxes associated with the Hawking temperature and assumption of black hole entropy, which are briefly reviewed. It is argued that the largest quantum effects arise from the conformal scalar degrees of freedom generated by the trace anomaly of the stress-energy tensor in curved space. At event horizons these can have macroscopically large backreaction effects on the geometry, potentially removing the classical event horizon of black hole and cosmological spacetimes, replacing them with a quantum phase boundary layer, where the effective value of the gravitational vacuum energy density can change. In the effective theory including the quantum effects of the anomaly, the cosmological term ? becomes a dynamical condensate, whose value depends upon boundary conditions at the horizon. By taking a positive value in the interior of a fully collapsed star, the effective cosmological term removes any singularity, replacing it with a smooth dark energy de Sitter interior. The resulting gravitational vacuum condensate star (or gravastar) configuration resolves all black hole paradoxes, and provides a testable alternative to black holes as the final quantum mechanical end state of complete gravitational collapse. The observed Λ_eff dark energy of our universe likewise may be a macroscopic finite size effect whose value depends not on Planck scale or other microphysics but on the cosmological Hubble horizon scale itself.

The current state of observational cosmology and the confrontation with theory is presented. The review is divided into the following sections:

• Basic observations on which the models are based.

• Testing the basic assumptions made in the construction of the standard cosmological models.

• Structure formation in the standard models

• Observational tests of the standard models - the confrontation with observation

• Basic problems and approaches to their solution

• Future challenges - the ESA EUCLID mission is given as an example.

Loop Quantum Gravity is a background independent, nonperturbative approach to the quantization of General Relativity. Its application to models of interest in cosmology and astrophysics, known as Loop Quantum Cosmology, has led to new and exciting views of the gravitational phenomena that took place in the early universe, or that occur in spacetime regions where Einstein's theory predicts singularities. We provide a brief introduction to the bases of Loop Quantum Cosmology and summarize the most important results obtained in homogeneous scenarios. These results include a mechanism to avoid the cosmological Big Bang singularity and replace it with a Big Bounce, as well as the existence of processes which favor inflation. We also discuss the extension of the frame of Loop Quantum Cosmology to inhomogeneous settings.

Numerical relativity simulations of non-vacuum spacetimes have reached a status where a complete description of the inspiral, merger and post-merger stages of the late evolution of close binary neutron systems is possible. Determining the properties of the black-hole-torus system produced in such an event is a key aspect to understand the central engine of short-hard gamma-ray bursts (sGRBs). Of the many properties characterizing the torus, the total rest-mass is the most important one, since it is the torus' binding energy which can be tapped to extract the large amount of energy necessary to power the sGRB emission. In addition, the rest-mass density and angular momentum distribution in the torus also represent important elements which determine its secular evolution and need to be computed equally accurately for any satisfactory modelling of the sGRB engine. In this paper we summarize our recent results from fully general-relativistic simulations of the coalescence of unequal-mass binary neutron stars, whose evolution is followed through the inspiral phase, the merger and prompt collapse to a black hole, up until the appearance of a thick accretion disk, which is studied as it enters a regime of quasi-steady accretion. Our simulations show that large-scale, quasi-Keplerian tori with masses as large as ∼ 0.2M can be produced as the result of the inspiral and merger of binary neutron stars with unequal masses.

Ground based GW detectors are limited at their lower frequency band (1-10 Hz) by settlement gravity gradients and seismic noise, and their sensitivity peaks at around 100 Hz. Sources in this band are mostly short duration signals, and their rates uncertain. Going down to milli-Hertz frequencies significantly increases the number and types of available sources. LISA was planned with the idea to explore a likely richer region of the GW spectrum, beyond that accessible to ground detectors; the latter are however expected to produce the first GW observations. In this paper I will present the main LISA concepts; in particular, emphasis will be placed on LISAPathFinder, the ESA precursor of LISA, in which our research group in Barcelona is heavily involved.

Some new aspects of axially symmetric spacetimes are discussed. These results open the door for future interplay between analytical and numerical studies. The new developments are based on the role of the total mass in axial symmetry. Finally, a list of relevant open problems is presented. These problems can be hopefully solved with an interaction between numerical and analytical insights.

A personal perspective on the interaction of analytical, numerical and computer algebra methods in classical Relativity is given. This discussion is inspired by the problem of the construction of invariants that characterise key solutions to the Einstein field equations. It is claimed that this kind of ideas will be or importance in the analysis of dynamical black hole spacetimes by either analytical or numerical methods.

We investigate the interior hyperbolic region of axisymmetric and stationary black holes surrounded by a matter distribution. First, we treat the corresponding initial value problem of the hyperbolic Einstein equations numerically in terms of a single-domain fully pseudo-spectral scheme. Thereafter, a rigorous mathematical approach is given, in which soliton methods are utilized to derive an explicit relation between the event horizon and an inner Cauchy horizon. This horizon arises as the boundary of the future domain of dependence of the event horizon. Our numerical studies provide strong evidence for the validity of the universal relation A⁺A⁻ = (8πJ)² where A⁺ and A⁻ are the areas of event and inner Cauchy horizon respectively, and J denotes the angular momentum. With our analytical considerations we are able to prove this relation rigorously.

This session is dedicated to the memory of Brian Edgar.

Semisymmetric spaces are a natural generalisation of symmetric spaces. For semisymmetric spaces in four dimensions with Lorentz signature, the Weyl tensor is easily seen (via spinors) to have a particularly simple quadratic property, which we call a special semisymmetric Weyl tensor. Using dimensionally dependent tensor identities, all (conformally) semisymmetric spaces are confirmed to have special semisymmetric Weyl tensors for all signatures in four dimensions. Furthermore, all Ricci-semisymmetric spaces with special semisymmetric Weyl tensors are shown to be semisymmetric for all signatures in four dimensions. Counterexamples demonstrate that these two properties have no direct generalisations in higher dimensions.

We find all Ricci semi-symmetric as well as all conformally semi-symmetric spacetimes. Neither of these properties implies the other. However, we find that for spacetimes (3+1 dim) with nonzero Weyl tensor and nonzero tracefree part of the Ricci tensor conformal semi-symmetry and Ricci semi-symmetry is equivalent.

We give a summary of recent results on the explicit local form of the second-order symmetric Lorentzian manifolds in arbitrary dimension, and its global version. These spacetimes turn out to be essentially a specific subclass of plane waves.

A review is given of results obtained in connection with perfect fluid spacetimes which are conformally related to Einstein spaces.

Special conformal Killing tensors have a number of interesting properties, an overview of which is given in the Riemannian case. Some of these properties remain valid in pseudo-Riemannian manifolds. Presently, we are investigating the latter problem, where, in order to obtain a better insight, we first examine some specific cases, such as special conformal Killing tensors in conformally flat or Petrov type D space-times.

Using extensions of the Newman-Penrose and Geroch-Held-Penrose formalisms to five dimensions, we invariantly classify all Petrov type D vacuum solutions for which the Riemann tensor is isotropic in a plane orthogonal to a pair of Weyl aligned null directions.

We find the complete solution of the Einstein-Maxwell field equations without sources for static spacetimes in which the space of Killing trajectories is conformally flat. The result is used to present an improved local characterisation of the Majumdar-Papapetrou class of solutions.

The growth of density perturbations in Kantowski-Sachs cosmologies with a positive cosmological constant is studied, using the 1+3 and 1+1+2 covariant formalisms. For each wave number a closed system for eight scalars is obtained. These are formed from quantities that are zero on the background and hence are gauge invariant. As an example a numerical solution describing the evolution of density perturbations on a background that experiences a bounce is presented. Typically the density gradient in the bouncing directions experiences a local maxium at or slightly after the bounce.

We use a contact geometric method to study Myers-Perry (MP) black holes in arbitrary dimensions with arbitrary angular momenta. We have shown that the MP black holes of dimension d with n equal nonzero spins and 2n ≥ d − 3 all have extremal limits as expected and that we should classify MP black holes in three series depending on whether the value of 2n − d + 3 is 0, 1 or 2. For black holes with 2n < d − 3 the Ruppeiner curvature diverges although they have no extremal limits. In order to have an ultraspinning mode at least one spin of the MP black hole must be set to zero. Our result agrees with others in the literature where the authors are able to establish the minimum temperature surface on which the membrane phase of ultraspinning MP black holes occurs. We conjecture that the membrane phase of ultraspinning MP black holes is reached around the minimum temperature in the case 2n < d − 3 which is where the Ruppeiner curvature diverges.

In the context of relativistic elasticity it is interesting to study axially symmetric space-times due to their significance in modeling neutron stars and other astrophysical systems of interest. To approach this problem, here, a particular class of these space-times is considered. A cylindrically symmetric elastic space-time configuration is studied, where the material metric is taken to be flat. The components of the energy-momentum tensor for elastic matter are written in terms of the invariants of the strain tensor, here chosen to be the eigenvalues of the pulled-back material metric. The Einstein field equations are presented and a condition confirming the existence of a constitutive function is obtained. This condition leads to special cases, in one of which a new system for the metric functions and an expression for the constitutive function are deduced. The new system depends on a particular function, which builds up the constitutive equation.

We outline the derivation of the Hawking quanta-partner signal in correlations, and highlight the specific application to detect it in density-density correlations in BECs.

We study the robustness of the spectrum emitted by an acoustic black hole by considering series of stationary flows that become either subsonic or supersonic, i.e. when the horizon disappears. We work with the superluminal Bogoliubov dispersion of Bose–Einstein condensates. We find that the spectrum remains remarkably Planckian until the horizon disappears. When the flow is everywhere supersonic, new pair creation channels open. This will be the subject of a forthcoming work.

Surface waves in classical fluids experience a rich array of black/white hole horizon effects. The dispersion relation depends on the characteristics of the fluid (in our case, water and silicon oil) as well as on the fluid depth and the wavelength regime. In some cases, it can be tuned to obtain a relativistic regime plus high-frequency dispersive effects. We discuss two types of ongoing analogue white-hole experiments: deep water waves propagating against a counter-current in a wave channel and shallow waves on a circular hydraulic jump.

We discuss recent work showing that in certain cases the membrane paradigm equations governing the dynamics of black hole horizons can be recast as relativistic conservation law equations. In the context of gauge/gravity dualities, these equations are interpreted as defining the viscous hydrodynamics of a holographically dual relativistic field theory. Using this approach, one can derive the viscous transport coefficients and the form of the entropy current for field theories dual to gravity plus matter fields.

We propose a dual lower dimensional description of the vacuum state associated to a strongly coupled CFT living on Rindler wedge slice close to the horizon hypersurface. From this field theory, with a linear response approach, we show the possibility to derive an entanglement horizon viscosity via a holographic Kubo formula in terms of a two-point function of the stress tensor of matter fields in the bulk. The entanglement viscosity over entropy density ratio come out to satisfy the universal Kovtun-Son-Starinets (KSS) value 1/4π in four dimensions, suggesting the universal ratio may be a fundamental property of quantum entanglement.

The paper outlines a theory where spacetime is treated as a physical four-dimensional continuum with properties similar to the ones of ordinary three-dimensional elastic continua. Two manifolds are compared: the first is flat; the second is curved and is thought as being obtained from the first by deformation. The intrinsic "rigidity" os spacetime implies that the deformation correspond to a strained state, where the strain tensor is given by half the difference between the metric tensor of the deformed and the undeformed manifolds. As it would happen in three dimensions the strain is associated with an elastic potential energy. The theory adds this deformation potential energy term to the standard spacetime Lagrangian density of General Relativity. Using the new Lagrangian density the theory is able to reproduce the accelerated expansion of the universe and is also consistent with the data from Big Bang Nucleosynthesis, the acoustic horizon of CMB and the structure formation after the recombination era.

In any static spacetime the quasilocal Tolman mass contained within a volume can be reduced to a Gauss-like surface integral involving the flux of a suitably defined generalized surface gravity. By introducing some basic thermodynamics, and invoking the Unruh effect, one can then develop elementary bounds on the quasilocal entropy that are very similar in spirit to the holographic bound, and closely related to entanglement entropy.

We apply the generalized second law of thermodynamics to discriminate among quantum corrections (whether logarithmic or power-law) to the entropy of the apparent horizon in spatially Friedmann-Robertson-Walker universes. We use the corresponding modified Friedmann equations along with either Clausius relation or the principle of equipartition of the energy to set limits on the value of a characteristic parameter entering the said corrections.

In this contribution we show that lorentzian dynamic wormholes emit thermal phantom-like radiation. Analogously to as it occurs for black holes, the consideration of such radiation process allows the formulation of a wormhole thermodynamics which might help in the understanding of those objects.

We are searching for the action principle for multiple M0–brane (multiple M-wave or mM0) system starting from the mM0 equations of motion obtained in the frame of superembedding approach. Surprisingly, the way from these equations to the action happens to be hampered by a problem which suggests a possible generalization of the action principle which we call "hierarchical action principle".

Hidden symmetries on curved space-times are investigated in connection with higher rank Killing tensors. It is shown that at the quantum level the conformal Killing vectors and tensors do not in general produce operators that commute with the Klein-Gordon operator.

We review the status of the integrability and solvability of the geodesics equations of motion on symmetric coset spaces that appear as sigma models of supergravity theories when reduced over respectively the timelike and spacelike direction. Such geodesic curves describe respectively timelike and spacelike brane solutions. We emphasize the applications to black holes.

The implementation of the dynamics in Loop Quantum Gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We use the recently introduced U(N) framework in order to construct SU(2) invariant operators and define a global U(N) symmetry that will select the homogeneous/isotropic states. Finally, we propose a Hamiltonian operator invariant under area-preserving deformations of the boundary surface and we identify possible connections of this model with Loop Quantum Cosmology.

A phase-space noncommutativity in the context of a Kantowski-Sachs cosmological model is considered to study the interior of a Schwarzschild black hole. Due to the divergence of the probability of finding the black hole at the singularity from a canonical noncommutativity, one considers a non-canonical noncommutativity. It is shown that this more involved type of noncommutativity removes the problem of the singularity in a Schwarzschild black hole.

We study numerically the formation of marginally closed trapped surfaces as the result of the collision of two shock gravitational waves in AdS in various dimensions (D = 4, 5, 6, 7 and 8). In all cases a critical value of the impact parameter is found above which no trapped surface of the type sought exists. We obtain a very simple scaling between the critical impact parameter and the energy of the incoming waves. The holographic implications of our results are discussed in the context of the AdS/CFT correspondence.

We investigate a formulation of continuum 4d gravity in terms of a constrained topological (BF) theory, in the spirit of the Plebanski formulation, but involving only linear constraints, of the type used recently in the spin foam approach to quantum gravity. We identify both the continuum version of the linear simplicity constraints used in the quantum discrete context and a linear version of the quadratic volume constraints that are necessary to complete the reduction from the topological theory to gravity. We illustrate and discuss also the discrete counterpart of the same continuum linear constraints. Moreover, we show under which additional conditions the discrete volume constraints follow from the simplicity constraints, thus playing the role of secondary constraints. Our analysis clarifies how the discrete constructions of spin foam models are related to a continuum theory with an action principle that is equivalent to general relativity.

Both the non-projectable and projectable version of Horava gravity face serious challenges. In the non-projectable version, the constraint algebra is seemingly inconsistent. The projectable version lacks a local Hamiltonian constraint, thus allowing for an extra graviton mode which can be problematic. A new formulation (based on arXiv:1007.1563) of Horava gravity which is naturally realized as a representation of the master constraint algebra (instead of the Dirac algebra) studied by loop quantum gravity researchers is presented. This formulation yields a consistent canonical theory with first class constraints; and captures the essence of Horava gravity in retaining only spatial diffeomorphisms as the physically relevant non-trivial gauge symmetry. At the same time the local Hamiltonian constraint is equivalently enforced by the master constraint.

Transverse Diffeomorphism (TDiff) theories are well-motivated theories of gravity from the quantum perspective, which are based upon a gauge symmetry principle. The main contribution of this work is to firmly establish a correspondence between TransverseDiff and the better-known scalar-tensor gravity — in its more general form —, a relation which is completely analogous to that between unimodular gravity and General Relativity. We then comment on observational aspects of TDiff. In connection with this proof, we derive a very general rule that determines under what conditions the procedure of fixing a gauge symmetry can be equivalently applied before the variational principle leading to the equations of motion, as opposed to the standard procedure, which takes place afterwards; this rule applies to gauge-fixing terms without derivatives.

The linearly polarized Gowdy T³ model can be regarded as compact Bianchi I cosmologies with inhomogeneous modes allowed to travel in one direction. We study a hybrid quantization of this model that combines the loop quantization of the Bianchi I background, adopting the improved dynamics scheme put forward by Ashtekar and Wilson-Ewing, with a Fock quantization for the inhomogeneities. The Hamiltonian constraint operator provides a resolution of the cosmological singularity and superselects separable sectors. We analyze the complicated structure of these sectors. In any of them the Hamiltonian constraint provides an evolution equation with respect to the volume of the associated Bianchi I universe, with a well posed initial value problem. This fact allows us to construct the Hilbert space of physical states and to show that we recover the standard quantum field theory for the inhomogeneities.

Loop Quantum Cosmology provides a successful quantization of isotropic and homogeneous flat universes with a massless, homogeneous scalar field as the matter content. Here, we propose a new ordering for the Hamiltonian constraint operator that facilitates the quantization of this model and makes the physical consequences much more transparent. In particular, our constraint is such that, in the gravitational sector, the zero volume state decouples, allowing us to get rid of the cosmological singularity already at a kinematical level, as well as to introduce a consistent densitization procedure for the constraint. Furthermore, the typical discretization of the spatial volume is achieved in superselection sectors which prove to be most suitable, with support on semilattices and where the basic functions that codify all the relevant information about the geometry have the expected Wheeler-DeWitt limit of standing waves. Thanks to these properties, we can demonstrate that the quantum bounce is generic for any physical state and superselection sector.

Quantum cosmology is usually studied quantizing symmetry-reduced variables. Is it possible, instead, to define quantum cosmology starting from the full quantum gravity theory? In Loop Quantum Gravity (LQG), it is possible to cut the degrees of freedom in a suitable way, in order to define a cosmological model. Such a model provides a tool for describing general fluctuations of the quantum geometry at the bounce that replaces the initial singularity. I focus on its simplest version, a "dipole" formed by two tetrahedra. This has been shown to describe a universe with anisotropic and inhomogenous degrees of freedom. Its dynamics can be given using the spinfoam formalism. I briefly review the present state of this approach.

The Bousso-Polchinski (BP) Landscape is a proposal for solving the Cosmological Constant Problem. The solution requires counting the states in a very thin shell in flux space. We find an exact formula for this counting problem which has two simple asymptotic regimes, one of them being the method of counting low Λ states given originally by Bousso and Polchinski. We finally give some applications of the extended formula: a robust property of the Landscape which can be identified with an effective occupation number, an estimator for the minimum cosmological constant and a possible influence on the KKLT stabilization mechanism.

In single-field, slow-roll inflationary models scalar and tensorial (Gaussian) perturbations are usually characterized by the so called power spectrum in momentum space. Even though these power spectra are finite and well define in momentum space, typical ultraviolet divergences in quantum field theory appear when these quantities are expressed in position space. The requirement of a finite variance in position space forces the introduction of regularization technics in quantum field theory in an expanding universe. The regularization process has an important impact on the predicted scalar and tensorial power spectra for wavelengths that today are at observable scales.

While moving down the potential on its classical slow roll trajectory, the inflaton field is subject to quantum jumps, which take it up or down the potential at random. In "stochastic inflation", the impact of these quantum jumps is modeled by smoothing out the field over (at least) Hubble-patch sized domains and treating fluctuations on smaller scales as noise. The inflaton thus becomes a stochastic process whose values at a given time are calculated using its probability distribution. We generalize this approach for non-canonic kinetic terms of Dirac Born Infeld (DBI) type and investigate the resulting modifications of the field's trajectory. Since models of DBI inflation arise from string-inspired scenarios in which the scalar field has a geometric interpretation, we insist that field value restrictions imposed by the model's string origin must be respected at the quantum level.

A gauge-invariant quantum theory of the flat Friedmann-Robertson-Walker (FRW) universe with dust is studied in terms of the Ashtekar variables. We use the reduced phase space quantization which has following advantages: (i) fundamental variables are all gauge invariant, (ii) there exists a physical time evolution of gauge-invariant quantities, so that the problem of time is absent and (iii) the reduced phase space can be quantized in the same manner as in ordinary quantum mechanics. Analyzing the dynamics of a wave packet, we show that the classical initial singularity is replaced by a big bounce in quantum theory.

It has recently been shown that f(R) theories formulated in the Palatini variational formalism are able to avoid the big bang singularity yielding instead a bouncing solution. The mechanism responsible for this behavior is similar to that observed in the effective dynamics of loop quantum cosmology and an f(R) theory exactly reproducing that dynamics has been found. I will show here that considering more general actions, with quadratic contributions of the Ricci tensor, results in a much richer phenomenology that yields bouncing solutions even in anisotropic (Bianchi I) scenarios. Some implications of these results will be discussed.

At the present work, it is studied the extension of F(R) gravities to the new recently proposed theory of gravity, the so-called Hořava-Lifshitz gravity, which provides a way to make the theory power counting renormalizable by breaking Lorentz invariance. It is showed that dark energy can be well explained in the frame of this extension, just in terms of gravity. It is also explored the possibility to unify inflation and late-time acceleration under the same mechanism, providing a natural explanation the accelerated expansion.

Motivated by string/M-theory predictions that scalar field couplings with the Gauss-Bonnet invariant, G, are essential in the appearance of non-singular early time cosmologies, we discuss the viability of an interesting alternative gravitational theory, namely, modified Gauss-Bonnet gravity, and present the viability bounds arising from the energy conditions. In particular, we consider a specific realistic form of f(G) analyzed in the literature that accounts for the late-time cosmic acceleration and that has been found to cure the finite-time future singularities present in the dark energy models, and further examine the respective viability of the specific f(G) model imposed by the weak energy condition.

We model the cosmological substratum by a viscous fluid that is supposed to provide a unified description of the dark sector and pressureless baryonic matter. In the homogeneous and isotropic background the total energy density of this mixture behaves as a generalized Chaplygin gas. The perturbations of this energy density are intrinsically non-adiabatic and source relative entropy perturbations. The resulting baryonic matter power spectrum is shown to be compatible with the 2dFGRS and SDSS (DR7) data. A joint statistical analysis, using also Hubble-function and supernovae Ia data, shows that, different from other studies, there exists a maximum in the probability distribution for a negative present value q₀ ≈ −0.53 of the deceleration parameter. Moreover, different from other approaches, the unified model presented here favors a matter content that is of the order of the baryonic matter abundance suggested by big-bang nucleosynthesis.

We consider a holographic cosmological model in which the infrared cutoff is fixed by the Ricci's length and dark matter and dark energy do not evolve separately but interact non-gravitationally with one another. This substantially alleviates the cosmic coincidence problem as the ratio between both components remains finite throughout the expansion. We constrain the model with observational data from supernovae, cosmic background radiation, baryon acoustic oscillations, gas mass fraction in galaxy clusters, the history of the Hubble function, and the growth function. The model shows consistency with observation.

We study the behavior of the parameter w(z) of the dark-energy equation of state, P_x = w(z)ρ_x, as function of the redshift data from GRBs, to check its deviations from its most accepted value of −1. To this end we first find a reasonable calibration for the GRB in order to extract the luminosity distance d_L as a function of the redshift. Then we proceed to calculate the Hubble function H(z) and w(z).

A central theme in cosmology is the perplexing fact that the Universe is undergoing an accelerating expansion. The latter, one of the most important and challenging current problems in cosmology, represents a new imbalance in the governing gravitational field equations. Several candidates, responsible for this expansion, have been proposed in the literature, in particular, dark energy models and modified gravity, amongst others. In this paper, we explore the possibility that the late-time cosmic acceleration is due to infra-red modifications of Einstein's theory of General Relativity, and review some of the modified theories of gravity that address this intriguing and exciting problem facing modern physics.

Recently a new type of cosmological singularity has been postulated for infinite barotropic index ω in the equation of state p = ωρ of the cosmological fluid, but vanishing pressure and density at the singular event. Apparently the barotropic index ω would be the only physical quantity to blow up at the singularity. In this talk we would like to discuss the strength of such singularities and compare them with other types. We show that they are weak singularities.

The generation of primordial gravitational waves is investigated within the hybrid quintessential inflationary model. Using the method of continuous Bogoliubov coefficients, we calculate the full gravitational-wave energy spectrum. The post-inflationary kination period, characteristic of quintessential inflationary models, leaves a clear signature on the spectrum, namely, a sharp rise of the gravitational-wave spectral energy density Ω_GW at high frequencies. For appropriate values of the parameters of the model, Ω_GW can be as high as 10⁻¹² in the MHz-GHz range of frequencies.

Annihilation of different dark matter (DM) candidates into Standard Model (SM) particles could be detected through their contribution to the gamma ray fluxes that are measured on the Earth. The magnitude of such contributions depends on the particular DM candidate, but certain imprints of produced photon spectra may be analyzed in a model-independent fashion. In this work we provide the fitting formulae for the photon spectra generated by WIMP annihilation into quarks, leptons and gauge bosons channels in a wide range of WIMP masses.

A possible process to destroy a black hole consists on throwing point particles with sufficiently large angular momentum into the black hole. In the case of Kerr black holes, it was shown by Wald that particles with dangerously large angular momentum are simply not captured by the hole, and thus the event horizon is not destroyed. Here we reconsider this gedanken experiment for black holes in higher dimensions. We show that this particular way of destroying a black hole does not succeed and that Cosmic Censorship is preserved.

We summarize the main features of a class of anomalous (asymptotically flat, but non Schwarzschild-like) gravitational configurations in models of gravitating non-linear electrodynamics (G-NED) whose Lagrangian densities are defined as arbitrary functions of the two field invariants and constrained by several physical admissibility conditions. This class of models and their associated electrostatic spherically symmetric black hole (ESSBH) solutions are characterized by the behaviours of the Lagrangian densities around the vacuum and at the boundary of their domain of definition.

Motion of free test particles in spacetimes of constant curvature with an expanding impulsive gravitational wave is completely described. Explicit formulae which identify the particle positions and velocities "in front of" and "behind" the impulse are derived for a general impulse of this type. As a particular example, the effect of spherical impulsive wave generated by a snapped cosmic string is analyzed and visualized.

Marginally outer trapped surfaces (MOTS) are routinely used as quasi-local replacements for black holes and it is expected that MOTS and event horizons should coincide in stationary and static spacetimes. In this short notice we present a uniqueness theorem of static spacetimes containing MOTS.

Although an event horizon defines a black hole, it is difficult to explain a boundary of dynamical black holes. A trapped surface is a candidate of the boundary of dynamical black holes, and is studied in various spacetimes and settings. Usually, there is no trapped surface in a Minkowski region, however, Bengtsson and Senovilla showed an interesting result as follows: in a four-dimensional self-similar Vaidya spacetime, they considered non-spherical trapped surfaces and showed that trapped surfaces can extend into the Minkowski region, if and only if a mass function rises fast enough [1]. We extend this result in a higher-dimensional spacetime, because recently studying higher-dimensional black holes is significant in the context of large extra dimensions or TeV-scale gravity. In this paper we investigate a higher-dimensional Vaidya spacetime with a self-similar mass function. We match two kinds of (n + 1)-surfaces and construct trapped surfaces extended into the Minkowski region by using Bengtsson and Senovilla's way. Moreover, we demonstrate that there is no naked singularity, if the spacetime has trapped surfaces as above. These results might become a foothold to define the boundary of dynamical black holes in higher-dimensional spacetimes.

We analyze the foundations of Finsler gravity theories with metric compatible connections constructed on nonholonomic tangent bundles, or (pseudo) Riemannian manifolds. There are considered "minimal" modifications of Einstein gravity (including theories with violation of local Lorentz invariance) and shown how the general relativity theory and generalizations can be equivalently re-formulated in Finsler like variables. We focus on Finsler branes solutions and perspectives in modern cosmology.

The Cabezas, Martín, Molina and Ruiz (CMMR) method allows us to build global analytic solutions of Einstein's equations for stationary isolated and rigidly rotating perfect fluid solutions. We start from a double approximation, postminkowskian and slow rotation, and end up getting a matched global solution from the inner and outer metrics. The metrics this way obtained have some uses. In particular, we will show the application of the scheme to the equation of state μ + (1 − n)p = μ₀ and how it can be applied to a build a source with two concentric comoving shells of fluid with different μ₀ We will also analyse the conditions under which this configuration can be a source of the Kerr metric.

The article written by C.M.Will (1974) describes a method how to obtain a perturbation of an (originally) Schwarzschild metric by a slowly rotating light ring. This scheme is revisited in order to adapt it to the case of a thin disc.It turns out for some class of mass distribution on the disc bounded between some radii the solution (or at least its decomposition into spherical harmonics) can be found explicitly.

The curvature invariants have been subject of recent interest in the context of the experimental detection of the gravitomagnetic field, namely due to the debate concerning the notions of "extrinsic" and "intrinsic" gravitomagnetism. In this work we explore the physical meaning of the curvature invariants, dissecting their relationship with the gravitomagnetic effects.

Strong-field gravitational plane waves are often represented in either the Rosen or Brinkmann forms. These forms are related by a coordinate transformation, so they should describe essentially the same physics, but the two forms treat polarization states quite differently. Both deal well with linear polarizations, but there is a qualitative difference in the way they deal with circular, elliptic, and more general polarization states. In this article we will describe a general algorithm for constructing arbitrary polarization states in the Rosen form.

Black hole highly-damped quasi-normal frequencies (QNFs) are very often of the form ω_n = (offset) + in (gap). We have investigated the genericity of this phenomenon for the Schwarzschild-deSitter (SdS) black hole by considering a model potential that is piecewise Eckart (piecewise Poschl–Teller), and developing an analytic "quantization condition" for the highly-damped quasi-normal frequencies. We find that the ω_n = (offset) + in (gap) behaviour is common but not universal, with the controlling feature being whether or not the ratio of the surface gravities is a rational number. We furthermore observed that the relation between rational ratios of surface gravities and periodicity of QNFs is very generic, and also occurs within different analytic approaches applied to various types of black hole spacetimes. These observations are of direct relevance to any physical situation where highly-damped quasi-normal modes are important.

When a stellar-mass compact object is captured by a supermassive black hole located in a galactic centre, the system losses energy and angular momentum by the emission of gravitational waves. Subsequently, the stellar compact object evolves inspiraling until plunging onto the massive black hole. These EMRI systems are expected to be one of the main sources of gravitational waves for the future space-based Laser Interferometer Space Antenna (LISA). However, the detection of EMRI signals will require of very accurate theoretical templates taking into account the gravitational self-force, which is the responsible of the stellar-compact object inspiral. Due to its potential applicability on EMRIs, the obtention of an efficient method to compute the scalar self-force acting on a point-like particle orbiting around a massive black hole is being object of increasing interest. We present here a review of our time-domain numerical technique to compute the self-force acting on a point-like particle and we show its suitability to deal with both circular and eccentric orbits.

Recent studies of modeling a progenitor of long gamma-ray bursts (LGRBs) suggest that progenitors of LGRBs might have a core with higher entropy than that of ordinary presupernove. Based on the above suggestion, we performed fully general relativistic, two-dimensional simulations of collapse of higher entropy core to a black hole and an accretion disk taking account of important microphysics. The initial core is simply modeled by a equilibrium configuration with constant entropy and electron fraction. We clarified that the formation dynamics depends even qualitatively on the amount of angular momentum. As a novel feature, we discovered that accretion disks formed after collapse can be convectively unstable.

We present results of general relativistic simulations of collapsing supermassive stars using the two-dimensional general relativistic numerical code Nada, which solves the Einstein equations written in the BSSN formalism and the general relativistic hydrodynamic equations with high resolution shock capturing schemes. These numerical simulations use a tabulated equation of state which includes effects of radiation and gas pressure, and those associated with the electron-positron pairs. We also take into account the effect of thermonuclear energy released by hydrogen and helium burning. We find that objects with mass ≈ 5 × 10⁵M and initial metallicity greater than Z_CNO ≈ 0.004 do explode if non-rotating, while the threshold metallicity for an explosion is reduced to Z_CNO ≈ 0.002 for objects uniformly rotating.

We analyze numerically the behaviour of the hyperbolic sector of the Fully Constrained Formulation (FCF) (Bonazzola et al. 2004). The numerical experiments allow us to be confident in the performances of the upgraded version of the CoCoNuT code (Dimmelmeier et al. 2005) by replacing the Conformally Flat Condition (CFC), an approximation of Einstein equations, by FCF. First gravitational waves in FCF in a dynamical spacetime with matter content will be shown.

Some of the most violent events in the universe, the gamma ray burst, could be related to the gravitational collapse of massive stellar cores. The recent association of long GRBs to some class of type Ic supernova seems to support this view. In such scenario fast rotation, strong magnetic fields and general relativistic effects are key ingredients. It is thus important to understand the mechanism that amplifies the magnetic field under that conditions. I present global simulations of the magneto-rotational collapse of stellar cores in general relativity and semi-global simulations of hydromagnetic instabilities under core collapse conditions. I discuss effect of the magneto-rotational instability and the magnetic field amplification during the collapse, the uncertainties in this process and the dynamical effects in the supernova explosion.

In this contribution, we discuss possible gravitational-wave (GWs) signatures emitted from core-collapse supernovae that do or do not produce explosions. For the former case, we study properties of GWs based on the three-dimensional (3D) supernova simulations, which demonstrate the neutrino-driven explosions aided by the standing accretion shock instability (SASI). By taking into account the effects of stellar rotation, we find that the gravitational waveforms from neutrinos in models that include rotation exhibit a common feature otherwise they vary much more stochastically in the absence of rotation. We point out that a recently proposed future space interferometers like Fabry-Perot type DECIGO would permit the detection of these signals for a Galactic supernova. For the black-hole forming supernovae, we study the GW emission based on a long-term special relativistic magnetohydrodynamic simulation in the light of collapsar model of long-duration gamma-ray bursts (GRBs). We find that the GWs from anisotropic neutrino emission illuminated by accretion disk become as high as the GWs contributed from matter motions of accreting material. These signals, possibly visible to the BBO-class detectors for a hundred Megaparsec distance scales, may give us an important probe into the central engines of GRBs.

We examine the non-axisymmetric Alfvén oscillations of relativistic stars with a strong dipole magnetic fields, where we have done the 2D simulation. We find that the spectrum of non-axisymmetric axial-type Alfvén oscillations is discrete as well as the axisymmetric polar Alfvén oscillations, in contrast to the spectrum of axisymmetric axial Alfvén oscillations which is continuum. We also show the dependence of Alvén frequency on the strength of magnetic field and find that such frequencies are smaller than those of the axisymmetric axial Alfvén oscillations. That is, to explain the observed evidence of quasi-periodic oscillations in the soft gamma repeaters, the non-axisymmetric axial oscillations could also play an important role.

We present the evolution of the full set of Einstein equations during preheating after inflation, for a generic supersymmetric model of hybrid inflation. Preheating of the scalar metric fluctuations does affect the evolution of vector and tensor modes, and in particular they do enhance the induced stochastic background of gravitational waves during preheating.This gives an energy density in general an order of magnitude larger than that obtained by evolving the tensors fluctuations in an homogeneous background metric. This enhancement can improve the expectations for detection by planned gravitational waves observatories.

The kinematic Sunyaev-Zeldovich effect produces a measurable temperature anisotropy in the cosmic microwave background that can be used to measure the bulk motion of clusters of galaxies. We discuss our recent measurement of motions on scales of ∼ 300–800 Mpc with amplitude and direction similar to the cosmological dipole, its systematics, uncertainties and the correlation with X-ray luminosity. The latter is a crucial test that supports the existence of the flow. We discuss the cosmological implications if the flow extends out to the cosmological horizon.

The specific angular momentum of a Kerr black hole must not be larger than its mass in the geometrical units. The observational confirmation of this bound which we call a Kerr bound directly suggests the existence of a black hole. On the other hand, the violation of this bound may suggest the existence of a superspinning object which might be suggested from a string theory argument. In order to investigate observational testability of this bound by using the X-ray energy spectrum of black hole candidates, we calculate the energy spectra from an optically thick and geometrically thin accretion disk of a superspinning object which is described by a Kerr metric but whose specific angular momentum is larger than its mass, and then compare the spectra of this object with those of a black hole. Based on this calculation, we present that the observational confirmation of the Kerr bound is very hard but the violation of it may be detectable if only the continuum X-ray spectrum of the disk is available.

The status of boson stars as black hole mimickers is presented among other mimickers. We focus on the analysis of the emission spectrum of a simple accretion disk model. We describe the free parameters that allow a boson star to become a black hole mimicker and present an example of a particular astrophysical case.

The scalar wave equation is considered in the background of a charged Vaidya metric in double null coordinates (u,v) describing a non-stationary charged black hole with varying mass m(v) and charge q(v). The resulting time-dependent quasinormal modes are presented and analyzed. We show, in particular, that it is possible to identify some signatures in the quasinormal frequencies from the creation of a naked singularity.

We study the chaotic features of time-like free motion around a Schwarzschild black hole, induced by the presence of a static, axially and reflectionally symmetric thin disc or ring. We describe the field by an exact (Weyl-type) solution of Einstein's equations and use Poincaré sections and time-series analysis in order to recognise overall tendencies in the evolution of phase portrait as well as changes that can be traced down to single orbits and their segments.

Introducing a surface layer of matter on the edge of a neutron star in slow rigid rotation, we analyze, from an intrinsic point of view, the junction conditions that must be satisfied between the interior and exterior solutions of the Einstein equations. In our model the core-crust transition pressure arise as an essential parameter in the description of a configuration. As an application of this formalism, we describe giant glitches of the Vela pulsar as a result of variations in the transition pressure, finding that these small changes are compatible with the expected temperature variations of the inner crust during glitch time

We discuss an extended version of electromagnetism in which the usual gauge fixing term is promoted into a physical contribution that introduces a new scalar state in the theory. This new state can be generated from vacuum quantum fluctuations during an inflationary era and, on super-Hubble scales, gives rise to an effective cosmological constant. The value of such a cosmological constant coincides with the one inferred from observations as long as inflation took place at the electroweak scale. On the other hand, the new state also generates an effective electric charge density on sub-Hubble scales that produces both vorticity and magnetic fields with coherent lengths as large as the present Hubble horizon.

An infinite family of relativistic finite thin disk model with magnetic field is presented. The model is obtained for solving the Einstein-Maxwell equations for static spacetimes by means of the Horský-Mitskievitch generating conjecture. The vacuum limit of these obtained solutions is the well known Morgan and Morgan solution. The obtained expressions are simply written in terms of oblate spheroidal coordinates. The mass of the disks are finite and the energy-momentum tensor agrees with all the energy conditions. The magnetic field and the circular velocity are evaluated explicitly. All the physical quantities obtained shown an acceptable behavior

Doubt is cast on the much quoted results of Yakupov that the torsion vector in embedding class two vacuum space-times is necessarily a gradient vector and that class 2 vacua of Petrov type III do not exist. The first result is equivalent to the fact that the two second fundamental forms associated with the embedding necessarily commute and has been assumed in most later investigations of class 2 vacuum space-times. Yakupov stated the result without proof, but hinted that it followed purely algebraically from his identity: R_ijklC^kl = 0 where C_ij is the commutator of the two second fundamental forms of the embedding.

From Yakupov's identity, it is shown that the only class two vacua with non-zero commutator C_ij must necessarily be of Petrov type III or N. Several examples are presented of non-commuting second fundamental forms that satisfy Yakupovs identity and the vacuum condition following from the Gauss equation; both Petrov type N and type III examples occur. Thus it appears unlikely that his results could follow purely algebraically. The results obtained so far do not constitute definite counter-examples to Yakupov's results as the non-commuting examples could turn out to be incompatible with the Codazzi and Ricci embedding equations. This question is currently being investigated.

New singularity theorems are proven in Lorentzian manifolds of arbitrary dimension n if they contain closed trapped submanifolds of arbitrary co-dimension. The timelike or null convergence conditions must be generalized to a condition on sectional curvatures, or tidal forces, which reduces to the former in the cases of co-dimension 1, 2 or n. Applications to higher dimensional theories and to the case of trapped circles are briefly mentioned.

By using the classical Hopf map, we construct another fibration that allows us to obtain examples of marginally trapped tori and marginally outer trapped tubes (MOTT) which are foliated by tori, all of them embedded in a closed Friedman-Lemaître-Robertson-Walker 4-spacetime. In addition, we show examples of MOTTs with any causal character.

We derive the horizon-entropy increase law for spherically symmetric quasi-local horizons in Brans-Dicke theory. The quasi-local horizons used do not marginally trap null rays, and hence are not apparent horizons or foliated by marginally trapped surfaces, but instead have instantaneously constant gravitational entropy in the outgoing null direction. The relation derived has a very direct comparison with the horizon-entropy increase law for event horizons.

How CYK tensors appear in General Relativity?

• Geometric definition of the asymptotic flat spacetime: strong asymptotic flatness, which guarantees well defined total angular momentum [2, 3, 4]

• Conserved quantities - asymptotic charges (, 𝓲⁰) [2, 3, 4, 5, 6, 9]

• Quasi-local mass and "rotational energy" for Kerr black hole [5]

• Constants of motion along geodesics and symmetric Killing tensors [5, 6]

Spacetimes possessing CYK tensor [10]:

• Minkowski (quadratic polynomials) [5]

• (Anti-)deSitter (natural construction) [7, 8, 9]

• Kerr (type D spacetime) [5]

• Taub-NUT (new symmetric conformal Killing tensors) [6]

Other applications:

• Symmetries of Dirac operator

• Symmetries of Maxwell equations

Algebraic conditions on the Ricci tensor in the Rainich-Misner-Wheeler unified field theory are known as the Rainich conditions. Penrose and more recently Bergqvist and Lankinen made an analogy from the Ricci tensor to the Bel-Robinson tensor B_αβμν, a certain fourth rank tensor quadratic in the Weyl curvature, which also satisfies algebraic Rainich-like conditions. However, we found that not only does the tensor B_αβμν fulfill these conditions, but so also does our recently proposed tensor V_αβμν, which has many of the desirable properties of B_αβμν. For the quasilocal small sphere limit restriction, we found that there are only two fourth rank tensors, B_αβμν and V_αβμν, which form a basis for good energy expressions. Both of them have the completely trace free and causal properties, these two form necessary and sufficient conditions. Surprisingly either completely traceless or causal is enough to fulfill the algebraic Rainich conditions.

The late-time behaviour of the Einstein-dust system is well understood for homogeneous spacetimes. For the case of Bianchi I we have been able to show that the late-time behaviour of the Einstein-Vlasov system is well approximated by the Einstein-dust system assuming that one is close to the unique stationary solution which is the attractor of the Einstein-dust system.

I propose a causality argument in order to solve the homogeneity (horizon) problem and the entropy problem of cosmology. The solution is based on the replacement of the spacelike Big Bang boundary with a null boundary behind which stays a chronology violating region. This solution requires a tilting of the light cones near the null boundary and thus it is based more on the behavior of the light cones and hence on causality than on the behavior of the scale factor (expansion). The connection of this picture with Augustine of Hippo famous philosophical discussion on time and creation is mentioned.

We review recent work on the stability of flat spatially homogeneous and isotropic backgrounds with a self-interacting scalar field. We derive a first order quasi-linear symmetric hyperbolic system for the Einstein-nonlinear-scalar field system. Then, using the linearized system, we show how to obtain necessary and sufficient conditions which ensure the exponential decay to zero of small non-linear perturbations.

Cylindrical-like coordinates for constant-curvature 3-spaces are introduced and discussed. This helps to clarify the geometrical properties, the coordinate ranges and the meaning of free parameters in the static vacuum solution of Linet and Tian. In particular, when the cosmological constant is positive, the spacetimes have toroidal symmetry. One of the two curvature singularities can be removed by matching the Linet–Tian vacuum solution across a toroidal surface to a corresponding region of the dust-filled Einstein static universe. Some other properties and limiting cases of these space-times are also described, together with their generalisation to higher dimensions.

A Lagrangian density is provided, that allows to derive the Z4 evolution system from a Palatini-type variation principle. The proposed action includes the supplementary vector Z_μ. The constraint Z_μ = 0 can be imposed just on the initial data, in order to recover true Einstein's solutions. This opens the door to analogous results for other numerical-relativity formalisms, like BSSN, that can be derived from Z4 by a symmetry-breaking procedure.

Well-posedness of the initial (boundary) value problem is an essential property, both of meaningful physical models and of numerical applications. To prove well-posedness of wave-type equations their level of hyperbolicity is an essential ingredient. We develop helpful tools and classify a large class of Hamiltonian versions of Einstein's equations with live gauge conditions with respect to their hyperbolicity. Finally we find a symmetric hyperbolic Hamiltonian formulation that allows for gauge conditions which are similar to the puncture gauge.

From the gauge/gravity duality to braneworld scenarios, black holes in compactified spacetimes play an important role in fundamental physics. Our current understanding of black hole solutions and their dynamics in such spacetimes is rather poor because analytical tools are capable of handling a limited class of idealized scenarios, only. Breakthroughs in numerical relativity in recent years, however, have opened up the study of such spacetimes to a computational treatment which facilitates accurate studies of a wider class of configurations. We here report on recent efforts of our group to perform numerical simulations of black holes in cylindrical spacetimes.

We present unequal mass head-on collisions of black holes in D = 5 dimensional space-times. We have simulated BH systems with mass ratios q = 1,1/2, 1/3, 1/4. We extract the total energy radiated throughout the collision and compute the linear momentum flux and the recoil velocity of the final black hole. The numerical results show very good agreement with point particle calculations when extrapolated to this limit.

A Relativistic Positioning System is defined by four clocks (emitters) broadcasting their proper time. Then, every event reached by the signals is naturally labeled by these four times which are the emission coordinates of this event. The coordinate hypersurfaces of the emission coordinates are the future light cones based on the emitter trajectories. For this reason the emission coordinates have been also named null coordinates or light coordinates. Nevertheless, other coordinate systems used in different relativistic contexts have the own right to be named null or light coordinates. Here we analyze when one can say that a coordinate is a null coordinate and when one can say that a coordinate system is null. Moreover, we examine the physical construction and the geometrical properties of several "null coordinate systems": the emission and the reception coordinates, the radar coordinates, and the Bondi-Sachs coordinates, among others.

In a previous work [Class. Quantum Grav.27 (2010) 065013] relativistic positioning systems in Minkowski space-time have been studied, and the transformation from emission to inertial coordinates have been obtained for an arbitrary configuration of the emitters. The formula giving this transformation applies in all the emission coordinate region and involves the orientation of the positioning system (the Jacobian sign of the map which gives the emission coordinates of an event). Nevertheless, there exists an inherent limitation on the applicability of this formula: only the users in the central region of a positioning system can obtain the orientation from the sole emission data. Here an observational method to determine the orientation of a relativistic positioning system is presented. In this procedure, a certain additional information allows any user to obtain its inertial coordinates, irrespectively of its location in the emission region of the positioning system.

We numerically implement the coordinate transformation between emission and inertial coordinates recently derived –in Minkowski space-time- by Coll et al. [1]. In order to carry out this transformation, we must know both proper times from four satellites and the inertial coordinates of these satellites when they emitted. It allows us to determine the position and the time coordinate of the receiver. Since we need to know the satellite positions at any time, we have simulated satellite constellations similar to those of GPS and Galileo global positioning system. All the satellite positions are calculated, at any time, with respect to an inertial frame with the origin at the Earth center. The orientation criterion described by the same authors [2] has been also implemented. The code has been appropiately tested and, then it has been applied to perform a preliminary study about the structure of the emission coordinate region and the grid region. The errors due to uncertainties in satellite positions have been also estimated.

The statistical distribution of caustic crossings by the images of a lensed quasar depends on the properties of the distribution of microlenses in the lens galaxy. We use a procedure based in Inverse Polygon Mapping to easily identify the critical and caustic curves generated by a distribution of stars in the lens galaxy. We analyze the statistical distributions of the number of caustic crossings by a pixel size source for several projected mass densities and different mass distributions. We compare the results of simulations with theoretical binomial distributions. Finally we apply this method to the study of the stellar mass distribution in the lens galaxy of QSO 2237+0305.

In recent years higher-dimensional black holes have attracted much interest because of various developments in gravity and high energy physics. But whereas higher-dimensional charged static (Tangherlini) and uncharged rotating (Myers-Perry) black holes were found long ago, black hole solutions of Einstein-Maxwell theory, are not yet known in closed form in more than 4 dimensions, when both electric charge and rotation are present. Here we therefore study these solutions and those of Einstein-Maxwell-dilaton theory, by using numerical and perturbative methods, and by exploiting the existence of spacetime symmetries. The properties of these black holes reveal new interesting features, not seen in D = 4. For instance, unlike the D = 4 Kerr-Newman solution, they possess a non-constant gyromagnetic factor.

We present a method of solving the Einstein equations under assumption of SO(n + 1) symmetry acting on n-dimensional spheres.

Geometric properties of higher dimensional Kerr-Schild (KS) spacetimes with (A)dS background are summarised. For Einstein spaces algebraic types of the Weyl tensor compatible with the KS ansatz are established, optical properties of the KS vector are given. Important examples of exact solutions belonging to this class, such as Kerr-de Sitter metrics in arbitrary dimension are also briefly discussed.

We show some physical properties of the systems of regular black diring(the regular gravitational systems with two S¹-rotational black rings arranged in concentric way in five-dimensional asymptotically flat spacetimes). Especially the existence of isothermal systems of black diring are shown, in which both isothermality and isorotation between the inner black ring and the outer black ring are realized. We also give some properties of the thermodynamic black di-ring including discussion about thermodynamic stabilities of the system.

We study stable bound orbits of a free particle around a black ring. Unlike the higher-dimensional black hole case, we find that there exist stable bound orbits in toroidal spiral shape near the ring axis and stable circular orbits on the axis. In addition, radii of stable bound orbits can be infinitely large if the ring thickness is less than a critical value.

It is shown that Born-Infeld gravity –a high energy deformation of Einstein gravity–removes the singularities of a cosmic string. The respective vacuum solution results to be free of conical singularity and closed timelike curves. The space ends at a minimal circle where the curvature invariants vanish; but this circle cannot be reached in a finite proper time.

In this paper we provide a possible realization of Penrose's idea of nonlinear gravitons by constructing a solution to the initial value constraints in Ashtekar variables. The solution inputs are a spatial SU(2) connection and two free functions of position, and can be constructed as a formal operatorial expansion in powers of the cosmological constant about spacetimes of Petrov Type O. We first present the linear case, and then provide a simple nonlinear example to first order using a spatially homogeneous connection.

We use conformal transformation to generate solutions of Einstein-Maxwell equations from other seed electro-vacuum spacetimes. We utilize the fact that the source-free Maxwell field is conformally invariant in four dimensions. Although the transformation is necessarily identical for most seed spacetimes, the pp-waves can be non-trivially transformed and may, therefore, play an analogous role as in the Birkhoff theorem.

We report on a group-theoretical revision of the Unruh effect based on the conformal group SO (4, 2), which has been developed by the authors and collaborators. Special Conformal Transformations (SCT) are interpreted as transitions to relativistic uniformly accelerated frames. Poincaré invariant θ-vacua (which turn out to be coherent states of conformal zero modes) are destabilized by SCT and radiate as a black body.

A certain vector-tensor theory of gravitation has been recently studied. In this theory, the zero-order energy density of the vector field could play the role of dark energy. In such a case, the question is: could the theory explain current cosmological observations as well as the so-called concordance model? Previous papers on the subject only consider a reduced number of current observations. We consider a wider set of observations including supernovae of type Ia, cosmic microwave background anisotropies, and the power spectrum of the energy density fluctuations. Results imply that, for negligible scalar perturbations of the vector field, the theory does not work.

The technique and some preliminary results about the study of the luminosity function (LF) of Lyman Alpha Emitters (LAEs) through gravitational lensing (GL) is presented. Clusters of galaxies, with suitably modeled gravitational lenses are observed using the tunable filters (TF) of the instrument OSIRIS at the GTC. The combination of these natural gravitational telescopes, and the higher contrast achievable by the TF, will allow the detection of very faint LAEs, not only reaching a step forward in understanding this primordial objects, but also achieving a better determination of the mass distribution on the inner regions of galaxy clusters.

We investigate static spherically symmetric vacuum solutions in the IR limit of projectable nonrelativistic quantum gravity, including the renormalisable quantum gravity recently proposed by Hořava, with an emphasis on the uniqueness of the solutions. It is found that the projectability condition plays an important role. Without the cosmological constant, the spacetime is uniquely given by the Schwarzschild solution. With the cosmological constant, the spacetime is uniquely given by the Kottler (Schwarzschild-(anti) de Sitter) solution for the entirely vacuum spacetime. However, in addition to the Kottler solution, the static spherical and hyperbolic universes are uniquely admissible for the locally empty region, for the positive and negative cosmological constants, respectively. This implies that static spherically symmetric entirely vacuum solutions would not admit the freedom to reproduce the observed flat rotation curves of galaxies.

We study the effect of the vacuum fluctuations of a massless conformally invariant field on tensor perturbations of spatially flat de Sitter spacetime. We find that de Sitter spacetime is stable within the regime of the semiclassical theory. Next we investigate the modification of linearized plane gravity waves by the effects of the quantum stress tensor. We find a correction term whose amplitude depends on the initial time η₀. If this initial time is the beginning of inflation, then as long as the energy scale of inflation and the proper frequency of the mode at η₀ are well below the Planck scale, the fractional correction is small. Nonetheless, modes which are transplanckian at the onset of inflation may have a significant correction. The increase in amplitude can be potentially observed through a modification of the power spectrum of tensor perturbations in inflationary cosmology. This enhancement of the power spectrum depends upon the initial time, and is greater for shorter wavelengths.

Away from critical curves, lens mapping can be seen as a linear invertible transformation of the plane even for regions (cells) of relatively large size. However, close to critical curves the departures from linearity can be very strong. We discuss the topological problems induced by the mapping of regions of the image plane that include critical curves (critical cells).

In the context of large extra-dimension or TeV-scale gravity scenarios, miniature black holes might be produced in collider experiments. In many works the validity of the cosmic censorship hypothesis has been assumed, which means that there is no chance to observe trans-Planckian phenomena in the experiments since such phenomena are veiled behind the horizons. Here, we argue that "visible borders of spacetime" (as effective naked singularities) would be produced, even dominantly over the black holes, in the collider experiments. Such phenomena will provide us an arena of quantum gravity.

The eventual production of mini black holes by proton-proton collisions at the LHC is predicted by theories with large extra dimensions resolvable at the Tev scale of energies. It is expected that these black holes evaporate shortly after its production as a consequence of the Hawking radiation. We show that for theories based on the ADS/CFT correspondence, the produced black holes may have an unstable horizon, which grows proportionally to the square of the distance to the collision point.

Determining the redshift of astronomical sources is fundamental for cosmological studies, since it allows deriving distances to the observer. However, the distance-redshift relationship commonly used is obtained from the isotropic, homogeneous Friedmann-Lemaitre-Robertson-Walker (FLRW) metric. By fitting this distance-redshift relations to Supernovae Ia data, used by many authors as standard candles for distance measurements, it was shown that the expansion of the universe is accelerating, since the addittion of equations of state in the cosmological model was required. Whether this dark energy is a cosmological constant or a quintessence is still to be determined, and is the objective of some current and future dark energy studies.

However, the Universe is not homogeneuos. The gravitational lens effect changes the luminosity of distant sources, and it may also change significantly the angular diameter distance, thus modifying the luminosity distance, changing the distance-redshift relation with respect to that of an homogeneous universe. This effect can be considered an additional source of dispersion of the data, affecting the determination of the dark energy equation of state.

We are developing a test for studying departures from the FLRW distance-redshift relation, and its impact on the determination of the dark energy equation of state.

In order to examine the rotational effect around neutron star in tensor-vector-scalar (TeVeS) theory, we consider the slowly rotating relativistic stars with a uniform angular velocity. As a result, we find that similar to the case in general relativity (GR), the angular momentum is proportional to the angular velocity and one could possibly distinguish the gravitational theory in the strong field regime even in the case that the value of the coupling constant K is quite small.

Many models in which the object under study loses all its mass have appeared in the literature. No doubt, the most eminent examples are the models for evaporating black holes and for evaporating stars. Here we describe a semiclassical study of these evaporating models centered on the evaporating event itself. We pay special attention to the evaporating models as a means of avoiding singularities during the collapse. In case of any pre-existing non-spacelike curvature singularity, we show that these models tend to evaporate it.