Highlights of 2011–2012

A typical galaxy is thought to contain tens of millions of stellar-mass black holes, the collapsed remnants of once massive stars, and a single nuclear supermassive black hole. Both classes of black holes accrete gas from their environments. The accreting gas forms a flattened orbiting structure known as an accretion disk. During the past several years, it has become possible to obtain measurements of the spins of the two classes of black holes by modeling the x-ray emission from their accretion disks. Two methods are employed, both of which depend upon identifying the inner radius of the accretion disk with the innermost stable circular orbit, whose radius depends only on the mass and spin of the black hole. In the Fe Kα method, which applies to both classes of black holes, one models the profile of the relativistically broadened iron line with a special focus on the gravitationally redshifted red wing of the line. In the continuum-fitting (CF) method, which has so far only been applied to stellar-mass black holes, one models the thermal x-ray continuum spectrum of the accretion disk. We discuss both methods, with a strong emphasis on the CF method and its application to stellar-mass black holes. Spin results for eight stellar-mass black holes are summarized. These data are used to argue that the high spins of at least some of these black holes are natal, and that the presence or absence of relativistic jets in accreting black holes is not entirely determined by the spin of the black hole.

Atom interferometers allow the measurement of the acceleration of freely falling atoms with respect to an experimental platform at rest on Earth's surface. Such experiments have been used to test the universality of free fall by comparing the acceleration of the atoms to that of a classical freely falling object. In a recent paper, Müller et al (2010 Nature 463 926–9) argued that atom interferometers also provide a very accurate test of the gravitational redshift (or universality of clock rates). Considering the atom as a clock operating at the Compton frequency associated with the rest mass, they claimed that the interferometer measures the gravitational redshift between the atom-clocks in the two paths of the interferometer at different values of gravitational potentials. In this paper, we analyze this claim in the frame of general relativity and of different alternative theories. We show that the difference of 'Compton phases' between the two paths of the interferometer is actually zero in a large class of theories, including general relativity, all metric theories of gravity, most non-metric theories and most theoretical frameworks used to interpret the violations of the equivalence principle. Therefore, in most plausible theoretical frameworks, there is no redshift effect and atom interferometers only test the universality of free fall. We also show that frameworks in which atom interferometers would test the redshift pose serious problems, such as (i) violation of the Schiff conjecture, (ii) violation of the Feynman path integral formulation of quantum mechanics and of the principle of least action for matter waves, (iii) violation of energy conservation, and more generally (iv) violation of the particle-wave duality in quantum mechanics. Standard quantum mechanics is no longer valid in such frameworks, so that a consistent interpretation of the experiment would require an alternative formulation of quantum mechanics. As such an alternative has not been proposed to date, we conclude that the interpretation of atom interferometers as testing the gravitational redshift at the Compton frequency is unsound.

Low mechanical loss, high index-of-refraction thin-film coating materials are of particular interest to the gravitational wave detection community, where reduced mirror coating thermal noise in gravitational wave detectors is desirable. Current studies are focused on understanding the loss of amorphous metal oxides such as SiO₂, Ta₂O₅ and HfO₂. Here, we report recent measurements of the temperature dependence of the mechanical loss of ion-beam sputtered hafnium dioxide (HfO₂) coatings that have undergone heat treatment. The results indicate that, even when partially crystallized, these coatings have lower loss than amorphous Ta₂O₅ films below ∼100 K and that their loss exhibits some features which are heat-treatment dependent in the temperature range of ∼100–200 K, with higher heat treatment yielding lower mechanical loss. The potential for using silica doping of hafnia coatings to prevent crystallization is discussed.

The Virgo gravitational wave detector is an interferometer (ITF) with 3 km arms located in Pisa, Italy. From July to October 2010, Virgo performed its third science run (VSR3) in coincidence with the LIGO detectors. Despite several techniques adopted to isolate the ITF from the environment, seismic noise remains an important issue for Virgo. Vibrations produced by the detector infrastructure (such as air conditioning units, water chillers/heaters, pumps) are found to affect Virgo's sensitivity, with the main coupling mechanisms being through beam jitter and scattered light processes. The Advanced Virgo design seeks to reduce ITF couplings to environmental noise by having most vibration-sensitive components suspended and in vacuum, as well as muffle and relocate loud machines. During the months of June and July in 2010, a Güralp-3TD seismometer was stationed at various locations around the Virgo site hosting major infrastructure machines. Seismic data were examined using spectral and coherence analysis with seismic probes close to the detector. The primary aim of this study was to identify noisy machines which seismically affect the ITF environment and thus require mitigation attention. Analyzed machines are located at various distances from the experimental halls, ranging from 10 to 100 m. An attempt is made to measure the attenuation of emitted noise at the ITF and correlate it with the distance from the source and with seismic attenuation models in soil.

We construct compact and high-accuracy reduced basis (RB) representations of single and multiple quasinormal modes (QNMs). The RB method determines a hierarchical and relatively small set of the most relevant waveforms. We find that the exponential convergence of the method allows for a dramatic compression of template banks used for ringdown searches. Compressing a catalog with a minimal match MM = 0.99, we find that the selected RB waveforms are able to represent any QNM, including those not in the original bank, with extremely high accuracy, typically less than 10⁻¹³. We then extend our studies to two-mode QNMs. Inclusion of a second mode is expected to help with detection, and might make it possible to infer details of the progenitor of the final black hole. We find that the number of RB waveforms needed to represent any two-mode ringdown waveform with the above high accuracy is smaller than the number of metric-based, one-mode templates with MM = 0.99. For unconstrained two modes, which would allow for consistency tests of general relativity, our high accuracy RB has around 10⁴ fewer waveforms than the number of metric-based templates for MM = 0.99. The number of RB elements grows only linearly with the number of multipole modes versus exponentially with the standard approach, resulting in very compact representations even for many multiple modes. The results of this paper open the possibility of searches of multi-mode ringdown gravitational waves.

Rapidly spinning neutron stars with non-axisymmetric mass distributions are expected to generate quasi-monochromatic continuous gravitational waves. While many searches for unknown, isolated spinning neutron stars have been carried out, there have been no previous searches for unknown sources in binary systems. Since current search methods for unknown, isolated neutron stars are already computationally limited, expanding the parameter space searched to include binary systems is a formidable challenge. We present a new hierarchical binary search method called TwoSpect, which exploits the periodic orbital modulations of the continuous waves by searching for patterns in doubly Fourier-transformed data. We will describe the TwoSpect search pipeline, including its mitigation of detector noise variations and corrections for Doppler frequency modulation caused by changing detector velocity. Tests on Gaussian noise and on a set of simulated signals will be presented.

This paper looks at how inhomogeneous spacetime models may be significant for cosmology. First it addresses how the averaging process may affect large-scale dynamics, with backreaction effects leading to effective contributions to the averaged energy–momentum tensor. Second, it considers how local inhomogeneities may affect cosmological observations in cosmology, possibly significantly affecting the concordance model parameters. Third, it presents the possibility that the universe is spatially inhomogeneous on Hubble scales, with a violation of the Copernican principle leading to an apparent acceleration of the universe. This could perhaps even remove the need for the postulate of dark energy.

Homogeneous, nearly-isotropic Bianchi cosmological models are considered. Their time evolution is expressed as a complete set of non-interacting linear modes on top of a Friedmann–Robertson–Walker background model. This connects the extensive literature on Bianchi models with the more commonly-adopted perturbation approach to general relativistic cosmological evolution. Expressions for the relevant metric perturbations in familiar coordinate systems can be extracted straightforwardly. Amongst other possibilities, this allows for future analysis of anisotropic matter sources in a more general geometry than usually attempted. We discuss the geometric mechanisms by which maximal symmetry is broken in the context of these models, shedding light on the origin of different Bianchi types. When all relevant length scales are super-horizon, the simplest Bianchi I models emerge (in which anisotropic quantities appear parallel transported). Finally we highlight the existence of arbitrarily long near-isotropic epochs in models of general Bianchi type (including those without an exact isotropic limit).

A gauge-invariant treatment of general-relativistic higher-order perturbations on generic background spacetime is proposed. After reviewing a general framework of the second-order gauge-invariant perturbation theory, we show the fact that the linear-order metric perturbation is decomposed into gauge-invariant and gauge-variant parts, which was the important premise of this general framework. This means that the development of the higher-order gauge-invariant perturbation theory on generic background spacetime is possible. A remaining issue to be resolved is also discussed.

We review an inflationary scenario with the anisotropic expansion rate. An anisotropic inflationary universe can be realized by a vector field coupled with an inflaton, which can be regarded as a counter example to the cosmic no-hair conjecture. We show the generality of anisotropic inflation and derive a universal property. We formulate cosmological perturbation theory in anisotropic inflation. Using the formalism, we show that anisotropic inflation gives rise to the statistical anisotropy in primordial fluctuations. We also explain a method to test anisotropic inflation using the cosmic microwave background radiation.

We critically assess the twin prospects of describing the observed universe in string theory, and using cosmological experiments to probe string theory. For the purposes of this short review, we focus on the limitations imposed by our incomplete understanding of string theory. After presenting an array of significant obstacles, we indicate a few areas that may admit theoretical progress in the near future.

Loop quantum cosmology (LQC) is the result of applying principles of loop quantum gravity (LQG) to cosmological settings. The distinguishing feature of LQC is the prominent role played by the quantum geometry effects of LQG. In particular, quantum geometry creates a brand new repulsive force which is totally negligible at low spacetime curvature but rises very rapidly in the Planck regime, overwhelming the classical gravitational attraction. In cosmological models, while Einstein's equations hold to an excellent degree of approximation at low curvature, they undergo major modifications in the Planck regime: for matter satisfying the usual energy conditions, any time a curvature invariant grows to the Planck scale, quantum geometry effects dilute it, thereby resolving singularities of general relativity. Quantum geometry corrections become more sophisticated as the models become richer. In particular, in anisotropic models, there are significant changes in the dynamics of shear potentials which tame their singular behavior in striking contrast to older results on anisotropies in bouncing models. Once singularities are resolved, the conceptual paradigm of cosmology changes and one has to revisit many of the standard issues—e.g. the 'horizon problem'—from a new perspective. Such conceptual issues as well as potential observational consequences of the new Planck scale physics are being explored, especially within the inflationary paradigm. These considerations have given rise to a burst of activity in LQC in recent years, with contributions from quantum gravity experts, mathematical physicists and cosmologists. The goal of this review is to provide an overview of the current state of the art in LQC for three sets of audiences: young researchers interested in entering this area; the quantum gravity community in general and cosmologists who wish to apply LQC to probe modifications in the standard paradigm of the early universe. In this review, effort has been made to streamline the material so that each of these communities can read only the sections they are most interested in, without loss of continuity.

The Galileons are a set of terms within four-dimensional effective field theories, obeying symmetries that can be derived from the dynamics of a (3 + 1)-dimensional flat brane embedded in a 5-dimensional Minkowski bulk. These theories have some intriguing properties, including freedom from ghosts and a non-renormalization theorem that hints at possible applications in both particle physics and cosmology. In this brief paper, we will summarize our attempts over the last year to extend the Galileon idea in two important ways. We will discuss the effective field theory construction arising from flat branes, of co-dimension greater than 1, embedded in a flat background—the multi-Galileons—and we will then describe symmetric covariant versions of the Galileons, more suitable for general cosmological applications. While all these Galileons can be thought of as interesting four-dimensional field theories in their own rights, the work described here may also make it easier to embed them into string theory, with its multiple extra dimensions and more general gravitational backgrounds.

I give a synthetic presentation of loop quantum gravity. I present the aims of the theory and compare the results obtained with the initial hopes that motivated the early interest in this research direction. I give my own perspective on the status of the program and attempt for a critical evaluation of its successes and limitations.

We give a definition of asymptotically locally Lifshitz spacetimes, with boundary data appropriate for a non-relativistic theory on the boundary. Solutions satisfying these boundary conditions are constructed in an asymptotic expansion. We identify the boundary data with sources for dual field theory operators, and give a prescription for calculating the one-point functions of the field theory operators (including the stress tensor) in the presence of arbitrary sources. The divergences in these one-point functions can be cancelled by holographic renormalization, adding counterterms which are local functions of the boundary data.

This paper is based on the invited talks delivered by the author at GR 19: the 19th International Conference on General Relativity and Gravitation (Ciudad de México, Mexico, July 2010).

I compute the Lorentzian EPRL/FK/KKL spinfoam vertex amplitude at the first order for regular graphs, with an arbitrary number of links and nodes, and coherent states peaked on a homogeneous and isotropic geometry. This form of the amplitude can be applied for example to a dipole with an arbitrary number of links or to the 4-simplex given by the complete graph on five nodes. All the resulting amplitudes have the same support, independently of the graph used, in the large-j (large-volume) limit. This implies that they all yield the Friedmann equation: I show this in the presence of the cosmological constant. This result indicates that in the semiclassical limit, quantum corrections in spinfoam cosmology do not come from just refining the graph, but rather from relaxing the large-j limit.

We generalize the SU(2) spinor framework of twisted geometries developed by Dupuis, Freidel, Livine, Speziale and Tambornino to the Lorentzian case, that is the group $SL(2,\mathbb {C})$. We show that the phase space for complex-valued Ashtekar variables on a spin-network graph can be decomposed in terms of twistorial variables. To every link there are two twistors—one to each boundary point—attached. The formalism provides a new derivation of the solution space of the simplicity constraints of loop quantum gravity. Key properties of the EPRL spinfoam model are perfectly recovered.

The holographic principle implies a vast reduction in the number of degrees of freedom of quantum gravity. This idea can be made precise in AdS₃, where the the stringy or gravitational exclusion principle asserts that certain perturbative excitations are not present in the exact quantum spectrum. We show that this effect is visible directly in the bulk gravity theory: the norm of the offending linearized state is zero or negative. When the norm is negative, the theory is signalling its own breakdown as an effective field theory; this provides a perturbative bulk explanation for the stringy exclusion principle. When the norm vanishes the bulk state is null rather than physical. This implies that certain non-trivial diffeomorphisms must be regarded as gauge symmetries rather than spectrum-generating elements of the asymptotic symmetry group. This leads to subtle effects in the computation of one-loop determinants for Einstein gravity, higher spin theories and topologically massive gravity in AdS₃. In particular, heat kernel methods do not capture the correct spectrum of a theory with null states.

Communicated by S Ross

The two-point function of linearized gravitons on de Sitter space is infrared divergent in the standard transverse traceless synchronous gauge defined by k = 0 cosmological coordinates (also called conformal or Poincaré coordinates). We show that this divergence can be removed by adding a linearized diffeomorphism to each mode function, i.e. by an explicit change of gauge. It follows that the graviton vacuum state is well defined and de Sitter invariant in agreement with various earlier arguments.

A recent precise formulation of the hoop conjecture in four spacetime dimensions is that the Birkhoff invariant β (the least maximal length of any sweepout or foliation by circles) of an apparent horizon of energy E and area A should satisfy β ⩽ 4πE. This conjecture together with the cosmic censorship or isoperimetric inequality implies that the length ℓ of the shortest non-trivial closed geodesic satisfies ℓ² ⩽ πA. We have tested these conjectures on the horizons of all four-charged rotating black hole solutions of ungauged supergravity theories and found that they always hold. They continue to hold in the presence of a negative cosmological constant, and for multi-charged rotating solutions in gauged supergravity. Surprisingly, they also hold for the Ernst–Wild static black holes immersed in a magnetic field, which are asymptotic to the Melvin solution. In five spacetime dimensions we define β as the least maximal area of all sweepouts of the horizon by two-dimensional tori, and find in all cases examined that , which we conjecture holds quiet generally for apparent horizons. In even spacetime dimensions D = 2N + 2, we find that for sweepouts by the product S¹ × S^{D − 4}, β is bounded from above by a certain dimension-dependent multiple of the energy E. We also find that ℓ^{D − 2} is bounded from above by a certain dimension-dependent multiple of the horizon area A. Finally, we show that ℓ^{D − 3} is bounded from above by a certain dimension-dependent multiple of the energy, for all Kerr–AdS black holes.

The elliptic Einstein–DeTurck equation may be used to numerically find Einstein metrics on Riemannian manifolds. Static Lorentzian Einstein metrics are considered by analytically continuing to Euclidean time. The Ricci–DeTurck flow is a constructive algorithm to solve this equation, and is simple to implement when the solution is a stable fixed point, the only complication being that Ricci solitons may exist which are not Einstein. Here we extend previous work to consider the Einstein–DeTurck equation for Riemannian manifolds with boundaries, and those that continue to static Lorentzian spacetimes which are asymptotically flat, Kaluza–Klein, locally AdS or have extremal horizons. Using a maximum principle, we prove that Ricci solitons do not exist in these cases and so any solution is Einstein. We also argue that the Ricci–DeTurck flow preserves these classes of manifolds. As an example, we simulate the Ricci–DeTurck flow for a manifold with asymptotics relevant for AdS₅/CFT₄. Our maximum principle dictates that there are no soliton solutions, and we give strong numerical evidence that there exists a stable fixed point of the flow which continues to a smooth static Lorentzian Einstein metric. Our asymptotics are such that this describes the classical gravity dual relevant for the CFT on a Schwarzschild background in either the Unruh or Boulware vacua. It determines the leading O(N²_c) part of the CFT stress tensor, which interestingly is regular on both the future and past Schwarzschild horizons.

This review provides some historical background and then reviews developments in string theory over the last 25 years or so. Both perturbative and non-perturbative approaches to string theory are surveyed and their impact on how we view quantum gravity is analysed.

We use the solution-generating technique, the TsT transformation, to obtain new solutions in type II string theory as well as in M-theory. We explicitly work out examples starting with rotating D3 and M2 branes as well as the D1–D5-p system. Among a variety of solutions, we find many of them having asymptotic Schrödinger symmetry. We also devise a new method of deriving the free energy of black brane systems, which is more efficient than the Euclidean action procedure. We test our method on known examples before applying it to new asymptotically Schrödinger backgrounds. We study the phase structure of these backgrounds by analyzing the free energy thus derived.

The quantum field theoretical prediction for the vacuum energy density leads to a value for the effective cosmological constant that is incorrect by between 60 and 120 orders of magnitude. We review an old proposal of replacing Einstein's field equations by their trace-free part (the trace-free Einstein equations), together with an independent assumption of energy–momentum conservation by matter fields. While this does not solve the fundamental issue of why the cosmological constant has the value that is observed cosmologically, it is indeed a viable theory that resolves the problem of the discrepancy between the vacuum energy density and the observed value of the cosmological constant. However, one has to check that, as well as preserving the standard cosmological equations, this does not destroy other predictions, such as the junction conditions that underlie the use of standard stellar models. We confirm that no problems arise here: hence, the trace-free Einstein equations are indeed viable for cosmological and astrophysical applications.

The Blandford–Znajek (BZ) mechanism has long been regarded as a key ingredient in models attempting to explain powerful jets in AGNs, quasars, blazzars, etc. In such a mechanism, energy is extracted from a rotating black hole and dissipated at a load at far distances. In this work we examine the behavior of the BZ mechanism with respect to different boundary conditions, revealing the robustness of the mechanism upon variation of these conditions. Consequently, this work closes a gap in our understanding of this important scenario.

We derive the Hamiltonian for spherically symmetric Lovelock gravity using the geometrodynamics approach pioneered by Kuchař (1994 Phys. Rev. D 50 3961) in the context of four-dimensional general relativity. When written in terms of the areal radius, the generalized Misner–Sharp mass and their conjugate momenta, the generic Lovelock action and Hamiltonian take on precisely the same simple forms as in general relativity. This result supports the interpretation of Lovelock gravity as the natural higher dimensional extension of general relativity. It also provides an important first step towards the study of the quantum mechanics, Hamiltonian thermodynamics and formation of generic Lovelock black holes.

We present a practical framework for ideal hyperelasticity in numerical relativity. For this purpose, we recast the formalism of Carter and Quintana as a set of Eulerian conservation laws in an arbitrary 3+1 split of spacetime. The resulting equations are presented as an extension of the standard Valencia formalism for a perfect fluid, with additional terms in the stress–energy tensor, plus a set of kinematic conservation laws that evolve a configuration gradient ψ^A_i. We prove that the equations can be made symmetric hyperbolic by suitable constraint additions, at least in a neighbourhood of the unsheared state. We discuss the Newtonian limit of our formalism and its relation to a second formalism also used in Newtonian elasticity. We validate our framework by numerically solving a set of Riemann problems in Minkowski spacetime, as well as Newtonian ones from the literature.

Various higher-dimensional black holes have been shown to be unstable by studying linearized gravitational perturbations. A simpler method for demonstrating instability is to find initial data that describes a small perturbation of the black hole and violates a Penrose inequality. An easy way to construct initial data is by conformal rescaling of the unperturbed black hole initial data. For a compactified black string, we construct initial data which violates the inequality almost exactly where the Gregory–Laflamme instability appears. We then use the method to confirm the existence of the 'ultraspinning' instability of Myers–Perry black holes. Finally, we study black rings. We show that 'fat' black rings are unstable. We find no evidence of any rotationally symmetric instability of 'thin' black rings.

A geometric inequality in general relativity relates quantities that have both a physical interpretation and a geometrical definition. It is well known that the parameters that characterize the Kerr–Newman black hole satisfy several important geometric inequalities. Remarkably enough, some of these inequalities also hold for dynamical black holes. This kind of inequalities play an important role in the characterization of the gravitational collapse; they are closely related with the cosmic censorship conjecture. Axially symmetric black holes are the natural candidates to study these inequalities because the quasi-local angular momentum is well defined for them. We review recent results in this subject and we also describe the main ideas behind the proofs. Finally, a list of relevant open problems is presented.

Bound inside rotating or charged black holes, there are stable periodic planetary orbits, which neither come out nor terminate at the central singularity. Stable periodic orbits inside black holes exist even for photons. These bound orbits may be defined as orbits of the third kind, following the Chandrasekhar classification of particle orbits in the black hole gravitational field. The existence domain for the third-kind orbits is rather spacious, and thus there is place for life inside supermassive black holes in the galactic nuclei. Interiors of the supermassive black holes may be inhabited by civilizations, being invisible from the outside. In principle, one can get information from the interiors of black holes by observing their white hole counterparts.

The null-timelike initial-boundary value problem for a hyperbolic system of equations consists of the evolution of data given on an initial characteristic surface and on a timelike worldtube to produce a solution in the exterior of the worldtube. We establish the well-posedness of this problem for the evolution of a quasilinear scalar wave by means of energy estimates. The treatment is given in characteristic coordinates and thus provides a guide for developing stable finite difference algorithms. A new technique underlying the approach has potential application to other characteristic initial-boundary value problems.

A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the harmonic formulation of Einstein's equations and a tetrad formulation of the Einstein–Bianchi system. However, a universal approach valid for other formulations is not in hand. In particular, there is no satisfactory boundary theory for the 3+1 formulations which have been highly successful in binary black hole simulation. I discuss the underlying problems that make the initial-boundary-value problem much more complicated than the Cauchy problem. I review the progress that has been made and the important open questions that remain.

Science is a differential equation. Religion is a boundary condition. (Alan Turing, quoted in J D Barrow, 'Theories of Everything')

An 'effective' quasi-local energy expression, motivated by the (relativistically corrected) Newtonian theory, is introduced in exact general relativity as the volume integral of all the source terms in the field equation for the Newtonian potential in static spacetimes. In particular, we exhibit a new post-Newtonian correction in the source term in the field equation for the Newtonian gravitational potential. In asymptotically flat spacetimes, this expression tends to the Arnowitt–Deser–Misner energy at spatial infinity as a monotonically decreasing set function. We prove its positivity in spherically symmetric spacetimes under certain energy conditions, and that its vanishing characterizes flatness. We argue that any physically acceptable quasi-local energy expression should behave qualitatively like this 'effective' energy expression in this limit.