Progress in Mathematical Relativity, Gravitation and Cosmology

Linear perturbations on Minkowski space are used to probe numerically the remote region of an asymptotically flat space-time close to spatial infinity. The study is undertaken within the framework of Friedrich’s conformal field equations and the corresponding conformal representation of spatial infinity as a cylinder. The system under consideration is the (linear) zero-rest-mass equation for a spin-2 field. The spherical symmetry of the underlying background is used to decompose the field into separate non-interacting multipoles. It is demonstrated that it is possible to reach null-infinity from initial data on an asymptotically Euclidean hyper-surface and that the physically important radiation field can be extracted accurately on

$${\mathcal{I}}^{+}$$

.

Lovelock theory is the natural extension of general relativity to higher dimensions. It can be also thought of as a toy model for ghost-free higher curvature gravity. It admits a family of AdS vacua, most (but not all) of them supporting black holes that display interesting features. This provides an appealing arena to explore different holographic aspects in the context of the AdS/CFT correspondence.

In this article we review the present status of the numerical construction of black holes in the Randall–Sundrum II braneworld model. After reviewing the new numerical methods to solve the elliptic Einstein equations, we numerically construct a black hole solution in five-dimensional anti-de Sitter (AdS

5

) space whose boundary geometry is conformal to the four-dimensional Schwarzschild solution. We argue that such a solution can be viewed as the infinite radius limit of a braneworld black hole, and we provide convincing evidence for its existence. By deforming this solution in AdS we can then construct braneworld black holes of various sizes. We find that standard 4

d

gravity on the brane is recovered when the radius of the black hole on the brane is much larger than the radius of the bulk AdS space.

We give an overview of four-dimensional BPS black holes in supergravity and string theory from both a macroscopic and a microscopic perspective.

The constraint equations are well-understood for hypersurfaces which are either everywhere non-null or null everywhere. The corresponding form of the equations is very different in both cases. In this paper, I discuss a general framework capable of analyzing the intrinsic and extrinsic geometry of general hypersurfaces of a spacetime. This framework is then applied to derive the form of the constraint equations in this general context. As an application, I will generalize the Israel equations for spacetime shells to the case when the shell is allowed to have varying causal character.

The Einstein–Straus model results from the embedding of a Schwarzs- child spherically symmetric region on a FLRW dust spacetime. It constituted the first, and most widely accepted, model to answer the question of the influence of large scale (cosmological) dynamics on local systems. The conclusion drawn by the model was that there is no influence from the cosmic background, since the spherical vacuole is static. However, apart from being highly inflexible, the model has been proved to be remarkably reluctant to admit non-spherical generalizations. This led us to consider the problem of the linearised perturbations of the Einstein–Straus model, first from a purely geometrical point of view. We now concentrate on imposing the Einstein field equations and in understanding the mixing between vector and tensor modes in the FLRW side, which arises as a consequence of the existence of an inner boundary. In particular, we analyse the relationship between exterior gravitational waves and the stationary and axial vacuum perturbations inside.

One way to understand more about spacetime singularities is to construct solutions of the Einstein equations containing singularities with prescribed properties. The heuristic ideas of the BKL picture suggest that oscillatory singularities should be very common and give a detailed picture of how these could look. The more straightforward case of singularities without oscillations is reviewed and existing results on that subject are surveyed. Then recent theorems proving the existence of spatially homogeneous solutions with oscillatory singularities of a specific type are presented. The proofs of these involve applications of some ideas concerning heteroclinic chains and their stability. Some necessary background from the theory of dynamical systems is explained. Finally some directions in which this research might be generalized in the future are pointed out.

We describe an approach to systematically generate regular and asymptotically flat dipole black rings in a 5D Einstein–Maxwell-dilaton theory obtained from 6D vacuum gravity by Kaluza–Klein reduction. Our construction employs the inverse scattering method in six dimensions. We illustrate the scheme with the explicit construction of the singly-spinning dipole ring. These techniques can also be used to generate more general five-dimensional black ring solutions, displaying rotation along the two orthogonal planes, electric charge and magnetic dipole charge.

Some of the basics of supersymmetric quantum cosmology are briefly reviewed, pointing to promising lines of research to explore.

We describe how the avoidance of the trans-Planckian problem of Hawking radiation can be used as a guiding principle in searching for a compelling scenario for the evaporation of black holes or black-hole-like objects. We argue that there exist only three possible scenarios, depending on whether the classical notion of long-lived horizon is preserved by high-energy physics and on whether the dark and compact astrophysical objects that we observe have long-lived horizons in the first place. Some specific findings along the way are (a) that a theory with high-energy superluminal signaling and a long-lived trapping horizon would be extremely unstable in astrophysical terms and (b) that stellar pulsations of objects hovering right outside, but extremely close to their gravitational radius, can result in a mechanism for Hawking emission.

In (2+1) space-time dimensions the Einstein theory of gravity has no local degrees of freedom. In fact, in the presence of a negative cosmological term, it is described by a (1+1) dimensional theory living on its boundary: Liouville theory. It is invariant under the action of the two-dimensional conformal group, which, in the gravitational context, corresponds to the asymptotic symmetries of asymptotically AdS geometries. In the flat case, when the cosmological term is turned off, a theory describing gravity at the boundary is absent. In this note we show that, in the Hamiltonian setup, such a theory may be constructed. The theory is BMS

3

invariant, as it should, corresponding to the asymptotic symmetry group of an asymptotically flat spacetime.

It is well known that the holographic Ricci dark energy can induce some future doomsdays in the evolution of the universe. Here we analyse the possible avoidance of those doomsdays by invoking a modification to general relativity on the form of curvature effects.

The construction of black-hole lattices, first attempted by Richard Lindquist and John Wheeler in 1957, has recently been tackled with renewed interest, as a test bed for studying the behavior of inhomogeneities in the context of the backreaction problem. In this contribution, I discuss how black-hole lattices can help shed light on two important issues, and illustrate the conclusions reached so far in the study of these systems.

We investigate the axial w quasi-normal modes of neutron stars for 18 realistic equations of state in order to study the influence of hyperons and quarks on the modes. The study has been developed with a new method based on Exterior Complex Scaling with variable angle, which allow us to generate pure outgoing quasi-normal modes. A complete study of the junction conditions has been done. We have obtained that w-modes can be used to distinguish between neutron stars with exotic matter and without exotic matter for compact enough stars.

We consider the quantization of a spherically symmetric gravitational system coupled to a massless scalar field within the loop quantum gravity framework. Our results rely on the uniform discretizations method developed during the last years. We minimize the associated discrete “master constraint” using a trial state whose gravitational part is peaked around the classical Schwarzschild solution.

We present an inflationary model preceded by a bounce in a metric

f

(

R

) theory. In this model, modified gravity affects only the early stages of the universe. We analyse the predicted spectrum of the gravitational waves in this scenario using the method of the Bogoliubov coefficients. We show that there are distinctive (oscillatory) signals on the spectrum for very low frequencies; i.e., corresponding to modes that are currently entering the horizon.

We report here on the results of Brax et al. (Phys. Rev. D 85:123516, 2012) where we consider the dynamics of a 3-brane embedded in an extra-dimensional Tolman–Bondi Universe where the origin of space plays a special role. We study the mirage cosmology on the probe brane, resulting in an inhomogeneous and anisotropic four dimensional cosmology where the origin of space is also special. We show that the induced geometry, which is initially inhomogeneous and anisotropic, converges to an isotropic and homogeneous Friedmann–Lemaitre 4d space-time around the origin of the spatial geometry. For example, when a 3-brane is embedded in a 5d matter dominated model, the 4d dynamics around the origin converge to a Friedmann–Lemaitre Universe in a radiation dominated epoch. We analyse this isotropisation process and show that it is a late time attractor.

Phase transitions between two competing vacua of a given theory are quite common in physics. We discuss how to construct the space-time solutions that allow the description of phase transitions between different branches (or asymptotics) of a given higher curvature gravity theory at finite temperature.

A constant-rate creation of dark particles in the late-time FLRW spacetime provides a cosmological model in accordance with precise observational tests. The matter creation backreaction implies in this context a vacuum energy density scaling linearly with the Hubble parameter, which is consistent with the vacuum expectation value of the QCD condensate in a low-energy expanding spacetime. Both the cosmological constant and coincidence problems are alleviated in this scenario. We discuss the cosmological model that arises in this context and present a joint analysis of observations of the first acoustic peak in the cosmic microwave background (CMB) anisotropy spectrum, the Hubble diagram for supernovas of type Ia (SNIa), the distance scale of baryonic acoustic oscillations (BAO) and the distribution of large scale structures (LSS). We show that a good concordance is obtained, albeit with a higher value of the present matter abundance than in the standard model.

What should be the quasinormal modes associated with a spacetime that contains a naked singularity instead of a black hole? In the present work we address this problem by studying the scattering of scalar fields on a curved background described by a Reissner–Nordström spacetime with

q

>

m

. We discuss the necessary conditions for the well-posedness of the problem, and give some numerical results for low

l

. The talk “Quasinormal modes from a naked singularity” was presented at the Spanish Relativity Meeting 2012 and was based on the results presented in Chirenti et al. (Phys. Rev. D 86:124008, 2012).

We present a model of gravity motivated by the Dirac–Born–Infeld type conformal scalar theory it yields when the Universe is conformally flat. We show that, if the Universe is permeated by a perfect fluid of radiation, the theory naturally predicts two eras of accelerated expansion mediated by a radiation dominated epoch, with a large hierarchy between the two effective cosmological constants, thus providing an alternative inflation scenario. This theory, dubbed

n

-DBI gravity, contains a preferred unit vector field, everywhere time-like, which breaks diffeomorphism invariance and gives rise to an extra scalar degree of freedom. We analyze the dynamics of this mode and conclude that it is free from some of the pathologies found in similar models, namely the issues of vanishing lapse short distance instability and strong coupling. We also show that the standard black holes of General Relativity are solutions of this theory.

We describe how to set up a perturbative framework to compute the metric in the future of a D-dimensional collision of two high speed black holes, by superimposing two equal Aichelburg–Sexl shock waves traveling, head-on, in opposite directions. We then estimate the radiation emitted in the collision using a D-dimensional generalisation of the Landau–Lifschitz pseudo-tensor—workable in a first order approach—and compute the percentage of the initial centre of mass energy emitted as gravitational waves. We shall see that our first order results are always within the bound obtained from apparent horizons computations.

We describe the generalisation to higher orders, of a perturbative framework to find the metric after the collision of two Aichelburg–Sexl gravitational shock waves in D-dimensions. A central challenge is to estimate the amount of gravitational radiation emitted in the collision, at higher orders. We present an adaptation of the Bondi mass loss formula in

D

-dimensions which is valid non-perturbatively, for axially symmetric asymptotically flat space-times. This is shown to coincide with the Landau–Lifshitz pseudo tensor result at first order in perturbation theory. We also discuss the validity of the method with a collision of charged shocks.

The location problem in relativistic positioning is considered in flat space-time. When two formal solutions are possible for a user (receiver) of the system, its true location may be obtained from a standard set of emission data extended with an observational rule. The covariant expression giving the location of the user in inertial coordinates is decomposed with respect to an inertial observer.

Brown introduced a covariant formulation of the BSSN equations well suited for curvilinear coordinate systems. We solve the BSSN equations in spherical symmetry and the general relativistic hydrodynamic equations written in flux-conservative form using a second-order partially implicit Runge–Kutta method to integrate the evolution equations without any regularization algorithm. Some tests assess the accuracy, numerical stability and expected convergence of the code.

A still not well understood feature of extended bodies in general relativity is the fact that their momentum is not, in general, parallel to the center of mass 4-velocity—the body is said to have “hidden momentum”. It can be split in two main types, a physical one that is gauge invariant, and the pure gauge hidden momentum that arises from the spin supplementary condition. In this paper I focus on the latter, using the formalism of gravitoelectromagnetism, which yields an easy way of understanding it, and under which conditions it arises.

We compare the results obtained from analytical perturbation theory and the AKM numerical code for an axistationary spacetime built from a rotating perfect fluid interior with the equation of state

$$\epsilon -3p = 4B$$

of the simple MIT bag model matched to an asymptotically flat exterior. We discuss the behaviour of the error in the metric components of the analytical approximation going to higher orders. Additionally, we check and comment the errors in multipole moments, central pressure and some other physical properties of the spacetime.

Thickness corrections to static, axisymmetric Dirac–Nambu–Goto branes embedded into spherically symmetric black hole spacetimes with arbitrary number of dimensions are studied. First, by applying a perturbative approximation, it is found that the thick solutions deviate significantly in their analytic properties from the thin ones near the axis of the system, and perturbative approaches around the thin configurations can not provide regular thick solutions above a certain dimension. For the general case, a non-perturbative, numerical approach is applied and regular solutions are obtained for arbitrary brane and bulk dimensions. As a special case, it has been found that two-dimensional branes are exceptional, as they share their analytic properties with the thin branes rather than the thick solutions of all other dimensions.

Extended electromagnetism (EE) has been applied to cosmology in various papers. In all of them, the zero order energy density of the EE vector field plays the same role as vacuum energy. Perturbations of this field have been studied by using different approaches. Firstly, some basic equations and ideas are summarized and, then, the CMBFAST code is used to calculate the cosmic microwave background angular power spectrum for appropriate values of the EE parameters. Comparisons of the resulting spectra with a good observational one compatible with WMAP7 (Wilkinson map anisotropy probe 7 years data) seem to be promising. We are currently looking for a set of parameters leading to the best fitting between the WMAP7 and EE spectra. Results will be presented elsewhere.

We are exploring the viability of the collapsar model for long-soft gamma-ray bursts. For this we perform state-of-the-art general relativistic hydrodynamic simulations in a dynamically evolving space-time with the CoCoNuT code. We start from massive low metallicity stellar models evolved up to core gravitational instability, and then follow the subsequent evolution until the system collapses forming a compact remnant. A preliminary study of the collapse outcome is performed by varying the typical parameters of the scenario, such as the initial stellar mass, metallicity, and rotational profile of the stellar progenitor. 1D models (without rotation) have been used to test our newly developed neutrino leakage scheme. This is a fundamental piece of our approach as it allows the central remnant (in all cases considered, a metastable high-mass neutron star) to cool down, eventually collapsing to a black hole (BH). In two dimensions, we show that sufficiently fast rotating cores lead to the formation of Kerr BHs, due to the fall-back of matter surrounding the compact remnant, which has not been successfully unbounded by a precedent supernova shock.

In the past century many exact solutions of Einstein’s field equations have been found and published. Some of these publications contain metrics which are

not

solutions of the Einstein field equations. This is due to typing errors in the one-forms or metrics, to the introduction of mysterious new coordinates after having carried out calculations in a different coordinate system or to the presentation of incorrect or incomplete solutions of some non-linear differential equations, etc. Also, many publications contain sets of supposedly different solutions to a given problem, which at a closer look can be seen to be special cases of others. As examples we look at the Newman Tamburino vacuum solutions and at the twisting type

D

solutions published by Frolov and Khlebnicov.

An arguable aspect of the modified gravity theories is that many of them present the so-called

degeneracy problem

. For instance, the cosmological evolution, gravitational collapse and the main features of standard black-hole configurations, can be mimicked by many of those theories. In this communication we revise briefly the appropriate observable quantities to be measured in order to discard alternative theories to

Λ

CDM, such as the observed growth of scalar perturbations with Sloan data and the CMB tensor perturbations evolution.

A brief summary of the new features and properties of four-dimensional charged black holes supported by general nonlinear models of electrodynamics minimally coupled to gravity, as compared to the usual Reissner–Nordström solution, is provided. These models are chosen as arbitrary function of the two field invariants and constrained by several physical admissibility requirements.

We consider holographic cosmological models of dark energy in which the infrared cutoff is set by the Hubble’s radius. We show that any interacting dark energy model, regardless of its detailed form, can be recast as a non interacting model in which the holographic parameter

c

2

evolves slowly with time. Two specific cases are analyzed. We constrain the parameters of both models with observational data, and show that they can be told apart at the perturbative level.

We quantize a perturbed Friedmann–Lemaître–Robertson–Walker model coupled to a massive scalar field. We consider only scalar perturbations, in a universe whose spatial sections have the topology of a three-sphere. The local gauge freedom is fixed at the classical level. We choose a preferred parametrization of the system by adapting uniqueness criteria for the quantization of scalar fields with time-dependent mass. The Hilbert space of the theory is constructed combining a polymer representation for the homogeneous background and the preferred Fock quantization for the perturbations. Finally, we propose a prescription to promote the Hamiltonian constraint to a quantum operator, and characterize the states annihilated by it in terms of their initial data at the minimum-volume section.

In this talk, we presented the null geodesics of the static charged black hole in heterotic string theory. The talk is based on a paper published in Physical Review D (Fernando, Phys. Rev. D 85:02403, 2012). In this paper, a detailed analysis of the geodesics are done in the Einstein frame as well as in the string frame. In the Einstein frame, the geodesics are solved exactly in terms of the Jacobi-elliptic integrals for all possible energy levels and angular momentum of the photons. In the string frame, the geodesics are presented for the circular orbits. As a physical application of the null geodesics, we have obtained the angle of deflection for the photons and the quasinormal modes of a massless scalar field in the eikonal limit.

We present some recent results in Flores et al. (ArXiv:1011.1154) about the relation between the causal boundary of standard stationary spacetimes (previously studied in Flores et al. (Memoirs A.M.S. ArXiv:1011.1154)) and that of a wide class of spacetimes which are isocausal to them.

Several years ago, we designed a particular ray tracing method. Combined with a Hydra parallel code (without baryons), it may compute some CMB anisotropies: weak lensing (WL) and Rees–Sciama (RS) effects. Only dark matter is fully necessary to estimate these effects. For very small angular scales, we made an exhaustive study leading to a lensing contribution slightly—but significantly—greater than previous ones. Afterwards, the same ray tracing procedure was included in a parallel Hydra code with baryons. The resulting code was then tested. This code is being currently applied to the study of the thermal and kinetic Sunyaev–Zel’dovich (SZ) contributions to the CMB anisotropies. We present here our first results.

We compute the Hawking radiation for a Proca field in the D-dimensional Schwarzschild background. We construct a numerical strategy to solve the coupled system which describes a coupling between two physical degrees of freedom of the field due to the mass term. We show how to define the transmission factors for the coupled system from an S matrix and compute them to generate the Hawking fluxes.

We investigate perturbations of Kantowski–Sachs models with a positive cosmological constant, using the gauge invariant 1 + 3 and 1 + 1 + 2 covariant splits of spacetime together with a harmonic decomposition. The perturbations are assumed to be vorticity-free and of perfect fluid type, but otherwise include general scalar, vector and tensor modes. In this case the set of equations can be reduced to six evolution equations for six harmonic coefficients.

Some theorems about the uniqueness of the energy of asymptotically Minkowskian spaces are recalled. The suitability of almost everywhere Gauss coordinates to define some kind of physical energy in these spaces is commented. Schwarzschild metric, when its source radius is larger than the Schwarzschild radius and in the case of a black hole, is considered. In both cases, by using a specific almost everywhere Gaussian coordinate system, a vanishing energy results. We explain why this result is not in contradiction with the quoted theorems. Finally we conclude that this metric is a particular case of what we have called elsewhere a

creatable universe

.

The infinitesimal transformations that leave invariant a two-covariant symmetric tensor are studied. The interest of these symmetry transformations lies in the fact that this class of tensors includes the energy-momentum and Ricci tensors. Moreover, all curvature collineations are necessarily Ricci collineations. We find that in most cases the class of infinitesimal generators of these transformations is a finite dimensional Lie algebra but also, in some cases exhibiting a higher degree of degeneracy, this class is infinite dimensional and may fail to be a Lie algebra.

Recent analytic results concerning stationary, self-gravitating fluids in Newtonian theory are discussed. We give a theorem that forbids infinitely extended fluids, depending on the assumed equation of state and the rotation law. This part extends previous results that have been obtained for static configurations. The second part discusses a Sobolev bound on the mass of the fluid and a rigorous Jeans-type inequality that is valid in the stationary case.

We formulate Penrose’s Weyl curvature hypothesis from an aspect of spacetime thermodynamics, which has been proposed by Jacobson. Using the evolution equation for the shear tensor of a null congruence in a local Rindler frame, we show that the entropy variation can be expressed in terms of the Weyl curvature. This result supports Penrose’s hypothesis, which claims that entropy of the gravitational field is somehow linked to the Weyl curvature. We point out that Penrose’s hypothesis corresponds to Clausius’ relation for a quasi-equilibrium state in spacetime thermodynamics.

It is shown that various pathological properties of spacetimes can be explained by the presence of negative mass, including the cases when the total mass of the solution is a positive quantity. As an illustration, we consider several well-known stationary axisymmetric vacuum and electrovac solutions of the Einstein–Maxwell equations. Our investigation naturally leads to a critique of the known maximal extensions of the Kerr and Kerr–Newman spacetimes which turn out to be neither analytic nor physically meaningful.

The Penrose inequality in terms of the Bondi mass at past null infinity can be approached with a method due to Ludvigsen and Vickers and clarified later on by Bergqvist (Ludvigsen and Vickers, J. Phys. A: Math. Gen. 16:3349–3353, 1983; Bergqvist, Class. Quantum Grav. 14:2577–2583, 1997). In this work, we apply the method to the special case of null shells of dust collapsing in a four-dimensional Minkowski background (Penrose construction, 1973). Our main conclusion is that the class of surfaces covered by the method is severely restricted. We provide afterwards a wide family of surfaces satisfying the Penrose inequality which includes the ones determined by the Bergqvist method.

We study approximation methods to construct physical solutions for the hybrid quantization of the Gowdy model with linear polarization and a massless scalar field. The loop quantization of the Bianchi I background and the presence of inhomogeneities lead to a very complicated Hamiltonian constraint. Therefore, the extraction of physical predictions calls for the introduction of well justified approximations. We show that, for specific regimes of physical interest, one can approximate the Hamiltonian constraint by a more simple one and obtain its solutions.

We consider several physical scenarios where black holes within classical gravity theories including

R

2

and Ricci-squared corrections and formulated à la Palatini can be analytically studied.

The notion of hole-free spacetime, initially introduced by Geroch, is reformulated, improved and commented. It is argued that any reasonable spacetime should satisfy it.

Using the theory of optimal rocket trajectories in general relativity, we present a candidate for the minimum total integrated acceleration closed timelike curve in the Godel universe, and give evidence for its minimality. The total integrated acceleration of this curve is lower than Malament’s conjectured value (Malament, 1984); however, Malament’s conjecture does seem to hold for periodic closed timelike curves.

We have been able to show that after a possible basis change the future of the non-diagonal Bianchi II and VI

0

spacetimes with collisionless matter is asymptotically diagonal assuming small data. More precisely these solutions are asymptotic to the Collins-Stewart solution with dust and the Ellis–MacCallum solution respectively.

We discuss the stability of static cosmological solutions in the framework of the dRGT theory of massive gravity (de Rham and Gabadadze, Phys. Rev. D82:044020, 2010). These solutions, only sourced by a perfect fluid, are either neutrally stable or unstable against spatially homogeneous and isotropic perturbations thus generalizing the Einstein static universe found in General Relativity. This paper summarises the results presented in (Phys Rev D 86:024035, 2012).

In the last years, the peculiar velocities of many X-ray galaxies clusters with respect to the distance have been measured directly in the rest frame of the cosmic microwave background radiation (CBR), using the kinematic Sunyaev–Zeldovich (kSZ) effect. These measures prove that exists a highly coherent motion, extending out to at least to 1

Gpc

, of the matter rest frame with respect to the CBR rest frame. This global motion was named “dark flow”. By using an inhomogeneous spherically symmetric “tilted” Lemaître model, we could explain the dark flow if we assume a linear increase with distance of the peculiar velocities, which is in principle allowed by these observations. This linear increase of the dark flow with the distance has the same behavior that the intrinsic dipole, due to the kinematic acceleration, which appears in the Hubble law of the Lemaître model. In the “tilted” Lemaître model considered, we consider that the radiation orthogonal congruence is a perfect fluid and the matter “tilted” congruence is an imperfect fluid with heat flux.

Generalised Teleparallel gravity, also referred to as

f

(

T

) gravity, has been recently proposed as an extended theory of gravitation able to give rise to an accelerated expansion in a matter only universe. We focus on two particular choices for

f

(

T

) and we check their viability contrasting the predicted background dynamics to the Hubble diagram as traced by both Type Ia Supernovae (SNeIa) and Gamma Ray Bursts (GRBs), the measurement of the rate expansion

H

(

z

), the Baryon Acoustic Oscillations (BAOs) at different redshifts, and the Cosmic Microwave Background Radiation (CMBR) distance priors. Both

f

(

T

) models turn out to be in very good agreement with this large dataset so that we also investigate whether it is possible to discriminate among them relying on the different growth factors.

We present a brief review of the modified Brans–Dicke theory (MBDT) in arbitrary dimensions, whereby the (

N

+ 1)-dimensional field equations reduce to the

N

-dimensional (

ND

) configuration with sources and an effective induced scalar potential. We then investigate a generalized Bianchi type I anisotropic cosmology in 5

D

BD theory that leads to an extended Kasner solution. By employing the original equations of MBDT, we probe the reduced Kasner cosmology on the hypersurface with proceeding the investigations for a few cosmological quantities, explaining their properties for some cosmological models.

The key paper that has served as the basis for the models describing the equilibrium configuration of a rotating isolated compact body using perturbation theory in General Relativity is due to Hartle (Astrophys J 150:1005–1029, 1967). Apart from a number of very restrictive explicit assumptions on the interior, the construction of the perturbed configuration hides some seemingly important implicit assumptions. In this work we focus on the study of these implicit assumptions, and therefore, on the rigorousness of the model. In order to do that we use a relatively recent framework following a proper theoretical analysis of a completely general perturbative approach to second order around static configurations of the exterior (asymptotically flat) vacuum problem of stationary and axisymmetric bodies with arbitrary matter content.

Gravity is understood as a geometrization of spacetime. But spacetime is also the manifold of the boundary values of the spinless point particle in a variational approach. The manifold of the boundary variables for any mechanical system, instead of being a Riemannian space it is a Finsler metric space such that the variational formalism can always be interpreted as a geodesic problem on this manifold. This manifold is just the flat Minkowski spacetime for the free relativistic point particle. Any interaction modifies its flat Finsler metric. In the spirit of unification of all forces, gravity cannot produce, in principle, a different and simpler geometrization than any other interaction. This implies that the basic assumption that what gravity produces is a Riemannian metric instead of a Finslerian one is a strong restriction so that general relativity can be considered as a low velocity limit of a more general gravitational theory.

A fast transition between a standard matter-like era and a late

Λ

CDM-like epoch generated by a single Unified Dark Matter component can explain the observed acceleration of the Universe. UDM models with a fast transition should be clearly distinguishable from

Λ

CDM (and alternatives) through observations. Here we focus on a particularly simple model and analyse its viability by studying features of the background model and properties of the adiabatic UDM perturbations.

The motion of the Galileo and GPS satellite constellations is simulated in Schwarzschild space-time, whereas photons travel in Minkowski space-time. This is a good enough approach to deal with the main goal of this paper: the study of positioning accuracy in the framework of the so-called relativistic positioning. Our study is based on numerical 4D simulations. In this meeting, the contribution of J.A. Morales-Lladosa contains some basic ideas which have been important to perform our numerical calculations. For four chosen emitters (satellites) of a certain constellation, many receivers located at different distances from Earth surface and in distinct directions are considered. Thus, we verify that, in some space-time regions, the Jacobian of the transformation giving the emission coordinate in terms of the inertial ones vanishes. For receivers placed close to these regions, positioning errors due to uncertainties in the satellite trajectories are too great. Our results suggest that, given a receiver, the 4-tuple of satellites used for location must be carefully chosen to minimize positioning errors (large enough Jacobian values).

In this work we introduce two new polynomial parametrizations of dark energy equation of state,

w

, and explore their correlation properties. The parameters to fit are the equation of state values at

z

= 0 and

z

= 0. 5, which have naturally low correlation and have already been shown to improve the popular Chevallier–Polarski–Linder (CPL) parametrization. We test our models with Type Ia Supernovae (SNeIa) and Baryon Acoustic Oscillations (BAO), in the form of both current and synthetic data. On one hand, we investigate the degree of improvement in dark energy constraints that can be achieved with future data. On the other hand, according to the Bayesian deviance information criterion (DIC), which penalizes large errors and correlations, we show that our models perform better than the CPL re-parametrization proposed by Wang (in terms of

z

= 0 and

z

= 0. 5). This is due to the combination of a lower correlation and smaller relative errors. The same holds for a frequentist perspective: our Figure-of-Merit is larger for our parametrizations.

Deformations of marginally outer trapped surfaces (MOTS) and tubes (MOTT) are studied by using the stability operator introduced by Andersson–Mars–Simon. Novel formulae for the principal eigenvalue are presented. The possibility of selecting a privileged MOTT is discussed. This is related to the concept of ‘core’ of black holes. In spherical symmetry the spherical MOTT is the boundary of a core. I argue how similar results may hold in general black-hole spacetimes.

CMB photons passing through a collapsing texture knot receive an energy shift, creating characteristic cold and hot spots on the sky. We calculate the anisotropy pattern produced by collapsing texture knots of arbitrary shape. The texture dynamics are solved numerically on a Minkowski background.

Using the invariant form of equation of geodesic deviation we analyze the relative deformations of a congruence of free test particles in general non-twisting, shearfree and expanding geometries. In four dimensions this class of exact solutions includes important classes of expanding gravitational waves. On the other hand, higher-dimensional Robinson–Trautman spacetimes can only be of algebraic type D. We emphasize the difference between the standard four-dimensional solutions and their arbitrary-dimensional extensions from the physical point of view of a geodesic observer.

We study connections between both event and quasilocal horizons and the algebraic type of the Weyl tensor. The relation regarding spacelike future outer trapping horizon is analysed in four dimensions using double-null foliation.

We study the gravitational collapse of a massless scalar field within the effective scenario of loop quantum gravity. Classical singularity is avoided and replaced by a quantum bounce in this model. It is shown that, quantum gravity effects predict a threshold scale bellow which no horizon can form as the collapse evolves towards the bounce.

It is shown that different pairs of stress-energy-momentum and spin tensors of quantum relativistic fields, which are commonly believed to be equivalent in special relativity, are in fact inequivalent. Different tensors imply different mean values of physical quantities like four-momentum and angular momentum density, and, in non-equilibrium situation, entropy production and transport coefficients. This result implies that specific stress-energy-momentum and spin tensors are physically meaningful even in the absence of gravitational coupling and raises the issue of finding the right pair (or the right class of pairs) of tensors. The existence of a non-vanishing spin tensor and, especially, a non symmetric stress-energy-momentum tensor would have major consequences in hydrodynamics, gravity and cosmology.

The aims of this work are (1) to sketch a proof that there are such parameterizations of the local frame and canonical connection structures when the gravitational field equations in f(R,T)-modified gravity, MG, can be integrated in generic off-diagonal forms with metrics depending on all spacetime coordinates and (2) to provide some examples of exact solutions.

I discuss conformally reducible but non-conformally flat space-times, which are solutions of the Einstein field equations with a perfect fluid source and for which the factor spaces are 2-spaces of constant curvature. These space-times are necessarily of Petrov type D. When the fluid velocity is aligned with the plane of principal null directions, they are locally rotationally symmetric of Stewart–Ellis class II and are determined up to two first order partial differential equations. When the fluid is non-aligned, the general solution can be given in terms of elementary functions.

We report on head-on collisions of charged black holes. We focus on non-spinning black holes, starting from rest and with the same charge to mass ratio

Q

∕

M

. The addition of charge to black holes introduces a new interesting channel of radiation and dynamics, most of which seem to be captured by Newtonian dynamics and flat-space intuition. The amount of gravitational-wave energy generated throughout the collision decreases by about three orders of magnitude as the charge-to-mass ratio

Q

∕

M

is increased from 0 to 0.98. This decrease is a consequence of the smaller accelerations present for larger values of the charge.

The extreme limit of the Kerr solution has recently attracted much attention, see (Compère, arXiv:1203.3561 [hep-th]) and references therein. We have investigated hypersurfaces called velocity-of-light surfaces for extreme and near extreme Kerr.

The linearised general conformal field equations in their first and second order form are used to study the behaviour of the spin-2 zero-rest-mass equation on Minkowski background in the vicinity of space-like infinity.

We derive conformally flat cylindrically symmetric solutions for spacetimes with a cosmological constant and investigate the matching problem of these solutions with the exterior Linet–Tian spacetime.

We analyze the phase structure of five-dimensional black di-ring in asymptotically flat vacuum gravity. We numerically plot the points of black di-rings in the phase diagram to search the region covered by black di-rings. The distribution of black di-ring shows that the area of black di-ring is always less than the maximum value of black ring. The plot indicates that there are black di-ring configurations whose area parameters are close to zero.

We revisit the issue on signatures of pre-inflationary background anisotropy by considering the quantization of a massless and minimally coupled scalar field in an axially symmetric Kasner background, mimicking cosmological perturbations. We show that the power spectrum of the scalar field fluctuation has a negligible difference from that in the standard inflation in the non-planar directions, but it has a sharp peak around the symmetry plane. This note is based on our recent paper (Kim and Minamitsuji, JCAP 1103:038, 2011).