Table of contents

We demonstrate that, if the usual phenomenological compactifications of IIB string theory with warped throats and anti-branes make sense, there must exist spherical brane shells in 4d that are overcharged. They correspond to classical over-extremal objects but without the usual naked singularities. The objects are made from D3-particles that puff into spherical five-branes that stabilise at finite radii in 4d and whose inside corresponds to the supersymmetric AdS vacuum. One can think of these shells as stabilised Brown–Teitelboim bubbles. We find that these objects can be significantly larger than the string scale depending on the details of the warped compactification.

The equivalence principle and its universality enables the geometrical formulation of gravity. In the standard formulation of General Relativity (GR) á la Einstein, the gravitational interaction is geometrized in terms of the spacetime curvature. However, if we embrace the geometrical character of gravity, two alternative, though equivalent, formulations of GR emerge in flat spacetimes, in which gravity is fully ascribed either to torsion or to non-metricity. The latter allows a much simpler formulation of GR oblivious to the affine spacetime structure, the Coincident General Relativity (CGR). The entropy of a black hole can be computed using the Euclidean path integral approach, which strongly relies on the addition of boundary or regulating terms in the standard formulation of GR. A more fundamental derivation can be performed using Wald's formula, in which the entropy is directly related to Noether charges and is applicable to general theories with diffeomorphism invariance. In this work we extend Wald's Noether charge method for calculating black hole entropy to spacetimes endowed with non-metricity. Using this method, we show that CGR with an improved action principle gives the same entropy as the well-known entropy in standard GR. Furthermore the first law of black hole thermodynamics holds and an explicit expression for the energy appearing in the first law is obtained.

A gauge invariant perturbation theory, based on the $1+1+2$ covariant split of spacetime, is used to study first order perturbations on a class of anisotropic cosmological backgrounds. The perturbations as well as the energy-momentum tensor are kept general, giving a system of equations on which different physical situations may be imposed. Through a harmonic decomposition, the system is then transformed to evolution equations in time and algebraic constraints. This result is then applied to dissipative one-component fluids, and on using the simplified acausal Eckart theory the system is reduced to two closed subsystems, governed by four and eight harmonic coefficients for the odd and even sectors respectively. The system is also seen to close in a simplified causal theory. It is then demonstrated, within the Eckart theory, how vorticity can be generated from viscosity.

Despite some 60 years of work on the subject of the Kerr rotating black hole there is as yet no widely accepted physically based and pedagogically viable ansatz suitable for deriving the Kerr solution without significant computational effort. (Typically involving computer-aided symbolic algebra.) Perhaps the closest one gets in this regard is the Newman–Janis trick; a trick which requires several physically unmotivated choices in order to work. Herein we shall try to make some progress on this issue by using a non-ortho-normal tetrad based on oblate spheroidal coordinates to absorb as much of the messy angular dependence as possible, leaving one to deal with a relatively simple angle-independent tetrad-component metric. That is, we shall write $g_\mathrm{ab} = g_{AB} \; e^{\,A}{}_a\; e^B{}_b$ seeking to keep both the tetrad-component metric g_AB and the non-ortho-normal co-tetrad $e^{\,A}{}_a$ relatively simple but non-trivial. We shall see that it is possible to put all the mass dependence into g_AB, while the non-ortho-normal co-tetrad $e^{\,A}{}_a$ can be chosen to be a mass-independent representation of flat Minkowski space in oblate spheroidal coordinates: $(g_\mathrm{Minkowski})_{ab} = \eta_{AB} \; e^{\,A}{}_a\; e^B{}_b$. This procedure separates out, to the greatest extent possible, the mass dependence from the rotational dependence, and makes the Kerr solution perhaps a little less mysterious.

We consider brane gravity as described by the Regge–Teitelboim geometric model, in any co-dimension. In brane gravity our spacetime is modelled as the time-like world volume spanned by a space-like brane in its evolution, seen as a manifold embedded in an ambient background Minkowski spacetime of higher dimension. Although the equations of motion of the model are well known, apparently their linearization has not been considered before. Using a direct approach, we linearize the equations of motion about a solution, obtaining the Jacobi equations of the Regge–Teitelboim model. They take a formidable aspect. Some of their features are commented upon. By identifying the Jacobi equations, we derive an explicit expression for the Morse index of the model. To be concrete, we apply the Jacobi equations to the study of the stability of a four-dimensional Schwarzschild spacetime embedded in a six-dimensional Minkowski spacetime. We find that it is unstable under small linear deformations.

The standard interpretation of observations such as the peak apparent magnitude of Type Ia supernova made from one location in a lumpy Universe is based on the idealised Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. All possible corrections to this model due to inhomogeneities are usually neglected. Here, we use the result from the recent concise derivation of the area distance in an inhomogeneous Universe to study the monopole and Hubble residual of the apparent magnitude of Type Ia supernovae. We find that at low redshifts, the background FLRW spacetime model of the apparent magnitude receives corrections due to relative velocity perturbation in the observed redshift. We show how this velocity perturbation could contribute to a variance in the Hubble residual and how it could impact the calibration of the absolute magnitude of the Type Ia supernova in the Hubble flow. We also show that it could resolve the tension in the determination of the Hubble rate from the baryon acoustic oscillation and local measurements.

We classify all self-dual Einstein four-manifolds invariant under a principal action of the three-dimensional Heisenberg group with non-degenerate orbits. This is of interest in the study of quantum-corrected gravitational physics, since they naturally arise as scalar manifolds of particular Lorentzian and Euclidean supergravities with one-loop corrections. The metrics are explicit and we find, in particular, that the Einstein constant can take any value. Then we examine when the corresponding (Riemannian or neutral-signature) metrics are (geodesically) complete. Finally, we exhibit the solutions of non-zero Ricci-curvature as different branches of one-loop deformed universal hypermultiplets in Riemannian and neutral signature.

Quantum particle creation from spacetime horizons, or accelerating boundaries in the dynamical Casimir effect, can have an equilibrium, or thermal, distribution. Using an accelerating boundary in flat spacetime (moving mirror), we investigate the production of thermal energy flux despite non-equilibrium accelerations, the evolution between equilibrium states, and the 'interference' between horizons. In particular, this allows us to give a complete solution to the particle spectrum of the accelerated boundary correspondence with Schwarzschild–de Sitter spacetime.

Sources of geophysical noise (such as wind, sea waves and earthquakes) or of anthropogenic noise impact ground-based gravitational-wave interferometric detectors, causing transient sensitivity worsening and gaps in data taking. During the one year-long third observing run (O3: from April 01, 2019 to March 27, 2020), the Virgo Collaboration collected a statistically significant dataset, used in this article to study the response of the detector to a variety of environmental conditions. We correlated environmental parameters to global detector performance, such as observation range, duty cycle and control losses. Where possible, we identified weaknesses in the detector that will be used to elaborate strategies in order to improve Virgo robustness against external disturbances for the next data taking period, O4, currently planned to start at the end of 2022. The lessons learned could also provide useful insights for the design of the next generation of ground-based interferometers.

We consider a semitetrad covariant decomposition of spherically symmetric spacetimes, and find a governing hyperbolic equation for the Gaussian curvature of two dimensional spherical shells, that emerges from the decomposition. The restoration factor of this hyperbolic travelling wave equation allows us to construct a geometric measure of complexity. This measure depends critically on the Gaussian curvature, and we demonstrate this geometric connection to complexity for the first time. We illustrate the utility of this measure by classifying well known spherically symmetric metrics with different matter distributions. We also define an order structure on the set of all spherically symmetric spacetimes, according to their complexity and physical properties.

The vacuum transition probabilities between to minima of a scalar field potential in the presence of gravity are studied using the Wentzel–Kramers–Brillouin approximation. First we propose a method to compute these transition probabilities by solving the Wheeler–DeWitt equation in a semi-classical approach for any model of superspace that contains terms of squared as well as linear momenta in the Hamiltonian constraint generalizing in this way previous results. Then we apply this method to compute the transition probabilities for a Friedmann–Lemaitre–Robertson–Walker (FLRW) metric with positive and null curvature and for the Bianchi III metric when the coordinates of minisuperspace obey a Standard Uncertainty Principle and when a Generalized Uncertainty Principle (GUP) is taken into account. In all cases we compare the results and found that the effect of considering a GUP is that the probability is enhanced at first but it decays faster so when the corresponding scale factor is big enough the probability is reduced. We also consider the effect of anisotropy and compare the result of the Bianchi III metric with the flat FLRW metric which corresponds to its isotropy limit and comment the differences with previous works.

The holographic principle suggests that the Hilbert space of quantum gravity is locally finite-dimensional. Motivated by this point-of-view, and its application to the observable Universe, we introduce a set of numerical and conceptual tools to describe scalar fields with finite-dimensional Hilbert spaces, and to study their behaviour in expanding cosmological backgrounds. These tools include accurate approximations to compute the vacuum energy of a field mode k as a function of the dimension d_k of the mode Hilbert space, as well as a parametric model for how that dimension varies with |k|. We show that the maximum entropy of our construction momentarily scales like the boundary area of the observable Universe for some values of the parameters of that model. And we find that the maximum entropy generally follows a sub-volume scaling as long as d_k decreases with |k|. We also demonstrate that the vacuum energy density of the finite-dimensional field is dynamical, and decays between two constant epochs in our fiducial construction. These results rely on a number of non-trivial modelling choices, but our general framework may serve as a starting point for future investigations of the impact of finite-dimensionality of Hilbert space on cosmological physics.

In two-dimensional string theory, a probe D0-brane does not see the black hole singularity due to a cancellation between its metric coupling and the dilaton coupling. A similar mechanism may work in the Schwarzschild black hole in large D dimensions by considering a suitable wrapped membrane. From the asymptotic observer, the wrapped membrane looks disappearing into nothing while the continuation of the time-like trajectory beyond the singularity suggests that it would reappear as an instantaneous space-like string stretching from the singularity. A null trajectory can be extended to a null trajectory beyond the singularity. Not only the effective particle but an effective string from the wrapped membrane can exhibit the same feature.

Making use of the $1 + 3$ covariant formalism, we show explicitly the effect that nonmetricity has on the dynamics of the Universe. Then, using the Dynamical System Approach, we analyze the evolution of Bianchi type-I cosmologies within the framework of $f(\mathcal{Q})$ gravity. We consider several models of function $f(\mathcal{Q})$, each of them manifesting isotropic eras of the Universe, whether transitional or not. In one case, in addition to the qualitative analysis provided by the dynamical system method, we also obtain analytical solutions in terms of the average length scale l.

In this work we examine the small mass limit of black holes (BHs), with and without spin, in theories where a scalar field is non-minimally coupled to a Gauss–Bonnet (GB) term. First, we provide an analytical example for a theory where a static closed-form solution with a small mass limit is known, and later use analytical and numerical techniques to explore this limit in standard scalar-GB theories with dilatonic, linear and quadratic-exponential couplings. In most cases studied here, we find an inner singularity that overlaps with the event horizon of the static BH as the small mass limit is reached. Moreover, since solutions in this limit possess a non-vanishing Hawking temperature, a naked singularity is expected to be reached through evaporation, raising questions concerning the consistency of these theories altogether. On the other hand, we provide for the first time in this context an example of a coupling where the small mass limit is never reached, thus preferred from the point of view of cosmic censorship. Finally, we consider BHs with spin and numerically investigate how this changes the picture, using these to place the tightest upper bounds to date on the coupling constant for the dilatonic and linear theories, with $\sqrt{\overline{\alpha}} \lt 1$ km.

We consider the massive Dirac equation in the exterior region of the five-dimensional Myers-Perry black hole. Using the resulting ordinary differential equations (ODEs) obtained from the separation of variables of the Dirac equation, we construct an integral spectral representation for the solution of the Cauchy problem with compactly supported smooth initial data. We then prove that the probability of presence of a Dirac particle to be in any compact region of space decays to zero as $t\to\infty$, in analogy with the case of the Dirac operator in the Kerr–Newman geometry (Finster et al 2003 Adv. Theor. Math. Phys.7 25–52).

We introduce the so-called static-fluid solutions in 2+1-dimensional spacetime. We assume the spacetime to be static and circular symmetric and for the perfect fluid we consider an equation of state (EoS) of the form $p\left(r\right) = -\frac{1}{3}\rho \left(r\right)$ where r is the radial coordinate. Since, unlike the 3+1-dimensions, in 2+1-dimensions there is no vacuum solution other than the flat spacetime, our approach is not exactly the same as the 3+1-dimensions such that the static-fluid is accompanied by a cosmological constant. In addition to that, at first, we present a static solution supported by a static-fluid of constant energy-momentum tensor with a general EoS. Then, in the nonconstant energy-momentum tensor case, we introduce a large class of solutions. Depending on the values of the integration constants it implies black holes, wormholes, or cosmological solutions. Some of these solutions are closed in two-space which are considered for the first time in 2+1-dimensions. In both cases i.e. the constant and nonconstant energy-momentum tensor we imposed the satisfaction of conservation of the energy-momentum i.e. $\nabla _{\mu}T^{\mu \nu} = 0$.