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We derive effective equations with loop quantum gravity corrections for the Lema\^itre-Tolman-Bondi family of space-times, and use these to study quantum gravity effects in the Oppenheimer-Snyder collapse model. For this model, after the formation of a black hole with an apparent horizon, quantum gravity effects become important in the space-time region where the energy density and space-time curvature scalars become comparable to the Planck scale. These quantum gravity effects first stop the collapse of the dust matter field when its energy density reaches the Planck scale, and then cause the dust field to begin slowly expanding. Due to this continued expansion, the matter field will eventually extend beyond the apparent horizon, at which point the horizon disappears and there is no longer a black hole. There are no singularities anywhere in this space-time. In addition, in the limit that edge effects are neglected, we show that the dynamics for the interior of the star of uniform energy density follow the loop quantum cosmology effective Friedman equation for the spatially flat Friedman-Lema\^itre-Robertson-Walker space-time. Finally, we estimate the lifetime of the black hole, as measured by a distant observer, to be $\sim (GM)^2/\ell_{\rm Pl}$., Comment: 10 pages, 1 figure. v2: Discussion extended, appendix added, v3: figure added, clarifications added, v4: typos corrected

We study thermodynamics of the parabolic Lemaitre-Tolman-Bondi (LTB) cosmology supported by a perfect fluid source. This model is the natural generalization of the flat Friedmann-Robertson-Walker (FRW) universe, and describes an inhomogeneous universe with spherical symmetry. After reviewing some basic equations in the parabolic LTB cosmology, we obtain a relation for the deceleration parameter in this model. We also obtain a condition for which the universe undergoes an accelerating phase at the present time. We use the first law of thermodynamics on the apparent horizon together with the Einstein field equations to get a relation for the apparent horizon entropy in LTB cosmology. We find out that in LTB model of cosmology, the apparent horizon's entropy could be feeded by a term, which incorporates the effects of the inhomogeneity. We consider this result and get a relation for the total entropy evolution, which is used to examine the generalized second law of thermodynamics for an accelerating universe. We also verify the validity of the second law and the generalized second law of thermodynamics for a universe filled with some kinds of matters bounded by the event horizon in the framework of the parabolic LTB model. © 2015 Chinese Physical Society and IOP Publishing Ltd.

In this article, the analysis of Tsallis holographic dark energy (which turns into holographic dark energy for a particular choice of positive non-additivity parameter δ) in modified f (T, B) gravity with the validity of thermodynamics and energy conditions for a homogeneous and isotropic FLRW Universe has been studied. The enlightenment of the field equation towards , made possible by the fact that the model is purely accelerating, corresponds to q = −0.54 (Mamon and Das 2017 Eur. Phys. J. C 77 49). The generalized second law of thermodynamics is valid not only for the same temperature inside the horizon, but also for the apparent horizon for a change in temperature. The essential inspiration driving this article is to exhibit the applicability that the holographic dark energy achieved from standard Tsallis holographic dark energy and the components acquired from f(T, B) gravity are identical for the specific bounty of constants. The analysis of energy conditions confirms that the weak energy condition and the null energy condition are fulfilled throughout the expansion, while violation of the strong energy condition validates the accelerated expansion of the Universe. With the expansion, the model becomes a quintessence dominated model. The dominant energy condition is not observed initially when the model is filled with genuine baryonic matter, whereas it appears when the model is in the quintessence dominated era.

The transformation from initial coordinates (v,r) of the Vaidya metric, with light coordinate v, to the more physical diagonal coordinates (t,r) is obtained and analyzed from the point of view of global geometry. The exact solutions have been obtained in the case of a linear form of the mass function m(v). In the diagonal coordinates under consideration, a narrow region has been revealed near the apparent horizon of the Vaidya accreting black hole, where the metric differs qualitatively from the Schwarzschild one and cannot be represented as a small perturbation of the Schwarzschild solution. The global geometry of the thick photon shell between the two (inner and outer) Schwarzschild regions is constructed and the corresponding matching conditions are discussed. The propagation of light beams in the Vaidya metric in the case of accretion is investigated and the time of the apparent horizon’s crossings is calculated.

In a recent work we have proved a weaker version of the Penrose inequality with angular momentum, in axially symmetric space-times, for a compact and connected minimal surface. In this previous work we use the monotonicity of Geroch energy on 2-surfaces along the inverse mean curvature flow and we obtain a lower bound for the ADM mass in terms of the area, the angular momentun and a particular measure of size of the minimal surface. In the present work, using similar techniques and the same measure of size, we extend and improve the previous result for a compact and connected outermost apparent horizon. For this case we use the monotonicity of Hawking energy, instead of Geroch energy, along the inverse mean curvature flow, and assume different conditions on the extrinsic curvature. This type of relations constitutes an important test to evaluate the cosmic censorship conjecture., Comment: arXiv admin note: text overlap with arXiv:1708.04646

The character of thermodynamics for theories of gravity with coupling between matter and geometry in the FLRW universe has been studied in this paper. The result shows that on the apparent horizon, both the temporal and spatial component of the Friedmann equations can be written as the form of the first law of thermodynamics in the conservative context, but some additional terms are appeared due to the matter-geometry coupling and the non-equilibrium in the system. Moreover, the derived generalized second law of thermodynamics can not be always held in our considering case, which is different from the one given in general relativity. The condition to protect it is obtained, when we consider results from observational data and numerical solutions.

Applying Clausius relation with energy-supply defined by the unified first law of thermodynamics formalism to the apparent horizon of a massive gravity model in cosmology proposed lately, the corrected entropic formula of the apparent horizon is obtained with the help of the modified Friedmann equations. This entropy-area relation, together with the identified Misner-Sharp internal energy, verifies the first law of thermodynamics for the apparent horizon with a volume change term for consistency. On the other hand, by means of the corrected entropy-area formula and the Clausius relation delta Q = TdS, where the heat flow delta Q is the energy-supply of pure matter projecting on the vector xi tangent to the apparent horizon and should be looked on as the amount of energy crossing the apparent horizon during the time interval dt and the temperature of the apparent horizon for energy crossing during the same interval is 1/(2 pi(r) over tilde (A)), the modified Friedmann equations governing the dynamical evolution of the universe are reproduced with the known energy density and pressure of massive graviton. The integration constant is found to correspond to a cosmological term which could be absorbed into the energy density of matter. Having established the correspondence of massive cosmology with the unified first law of thermodynamics on the apparent horizon, the validity of the generalized second law of thermodynamics is also discussed by assuming the thermal equilibrium between the apparent horizon and the matter field bounded by the apparent horizon. It is found that, in the limit H-c -> 0, which recovers the Minkowski reference metric solution in the flat case, the generalized second law of thermodynamics holds if alpha(3) + 4 alpha(4) < 0. Without this condition, even for the simplest model of dRGT massive cosmology with alpha(3) = alpha(4) = 0, the generalized second law of thermodynamics could be violated.

Using Parikh's tunneling method, the Hawking radiation on the apparent horizon of a Vaidya–Bonner black hole is calculated. When the back-reaction of particles is neglected, the thermal spectrum can be precisely obtained. Then, the black hole thermodynamics can be calculated successfully on the apparent horizon. When a relativistic perturbation is applied to the apparent horizon, a similar calculation can also lead to a purely thermal spectrum. The first law of thermodynamics can also be derived successfully at the new supersurface near the apparent horizon. When the event horizon is thought of as a deviation from the apparent horizon, the expressions of the characteristic position and temperature are consistent with the previous viewpoint which asserts that the thermodynamics should be based on the event horizon. It is concluded that the thermodynamics should be constructed exactly on the apparent horizon while the event horizon thermodynamics is just one of the perturbations near the apparent horizon.

We investigate the possibility of cosmic censorship violation in the gravitational collapse of radiating dyon solution. It is shown that the final outcome of the collapse depends sensitively on the electric and magnetic charge parameters. The graphs of the outer apparent horizon, inner Cauchy horizon for different values of parameters are drawn. It is found that the electric and magnetic components push the apparent horizon towards the retarded time-coordinate axis, which in turn reduces the radius of the apparent horizon in Vaidya spacetime. Also, we extend the earlier work of Chamorro and Virbhadra [Pramana, J. Phys. 45 (1995) 181].

For a stable, marginally outer trapped surface (MOTS) in an axially symmetric spacetime with cosmological constant λ > 0 and with matter satisfying the dominant energy condition, we prove that the area A and the angular momentum J satisfy the inequality 8π|J| ≤ A√(1 - λA/4π)(1 - λA/12π), which is saturated precisely for the extreme Kerr-de Sitter family of metrics. This result entails a universal upper bound |J| ≤ Jmax ≈ 0.17/λ for such MOTS, which is saturated for one particular extreme configuration. Our result sharpens the inequality 8π |J| ≤ A (Dain and Reiris 2011 Phys. Rev. Lett. 107 051101, Jaramillo, Reiris and Dain 2011 Phys. Rev. Lett. D 84 121503), and we follow the overall strategy of its proof in the sense that we first estimate the area from below in terms of the energy corresponding to a 'mass functional', which is basically a suitably regularized harmonic map S2 → H2. However, in the cosmological case this mass functional acquires an additional potential term which itself depends on the area. To estimate the corresponding energy in terms of the angular momentum and the cosmological constant we use a subtle scaling argument, a generalized 'Carter-identity', and various techniques from variational calculus, including the mountain pass theorem. Fil: Gabach Clement, Maria Eugenia. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina Fil: Reiris, Martín. Max Planck Fuer Gravitationsphysik (aei); Alemania Fil: Simon, Walter. Universidad de Viena; Austria

Higher-dimensional scenarios allow for the formation of mini-black holes from TeV-scale particle collisions. The purpose of this paper is to review and compare different methods for the estimate of the total gravitational energy emitted in this process. To date, black hole formation has mainly been studied using an apparent horizon search technique. This approach yields only an upper bound on the gravitational energy emitted during black hole formation. Alternative calculations based on instantaneous collisions of point particles and black hole perturbation theory suggest that the emitted gravitational energy may be smaller. New and more refined methods may be necessary to accurately describe black hole formation in high-energy particle collisions., 6 pages, ReVTeX 4. Minor corrections and some relevant references added

In this paper, we investigate the effects of a new version of the generalized uncertainty principle (modified GUP) on the dynamics of the Universe. As the modified GUP will modify the relation between the entropy and area of the apparent horizon, it will also deform the Friedmann equations within Jacobson's approach. We explicitly find these deformed Friedmann equations governing the modified GUP-corrected dynamics of such a Universe. It is shown that the modified GUP-deformed Jacobson's approach implies an upper bound for the density of such a Universe. The Big Bang singularity can therefore also be avoided using the modified GUP-corrections to horizons' thermodynamics. In fact, we are able to analyze the pre Big Bang state of the Universe. Furthermore, the equations imply that the expansion of the Universe will come to a halt and then will immediately be followed by a contracting phase. When the equations are extrapolated beyond the maximum rate of contraction, a cyclic Universe scenario emerges., Comment: 20 pages, 2 figures. Matches the published version

The objective of this paper is to investigate the thermodynamic properties of McVittie universe. It turns out that the Einstein field equations are obtained by using Clausius equation near apparent horizon of McVittie universe. For the existence of horizons, different conditions in terms of McVittie parameters are discussed. Diverse cases of surface gravity are studied and conditions in terms of parameters for which surface gravity is positive, zero and negative are obtained and analyzed. It is shown that the generalized second law (GSL) holds near the apparent horizon if ${\dot{R}}_{A}\gt 0$. Our results show that the heat capacity, C P , of the universe is always negative for matter dominated phase having P = 0. On the other hand, when $P\gt 0$, the heat capacity ${C}_{P}\gt 0$ provided ${R}_{A}\gt \sqrt{2}/\sqrt{8\pi P-3{H}^{2}}$ and negative otherwise. Furthermore, when $P\gt 0$, the temperature of the universe is minimum at ${R}_{\min }=\sqrt{2}/\sqrt{8\pi P-3{H}^{2}}$ while its heat capacity diverges.

We propose a generally covariant version of the Schrodinger equation suitable for general relativity by quantizing the geodesic deviation equation. The resulting wave equation depends on the (geodesic) trajectory of the observer. It is first order in `time' and second order in the `spatial' derivatives. In the following we apply our prescription to quantum tunnelling from beyond the event horizon of a spherical symmetric (Schwarzschild) black hole.

We describe results of a numerical calculation of circularly symmetric scalar field collapse in three spacetime dimensions with negative cosmological constant. The procedure uses a double null formulation of the Einstein-scalar equations. We see evidence of black hole formation on first implosion of a scalar pulse if the initial pulse amplitude $A$ is greater than a critical value $A_*$. Sufficiently near criticality the apparent horizon radius $r_{AH}$ grows with pulse amplitude according to the formula $r_{AH} \sim (A-A_*)^{0.81}$., Comment: 10 pages, 1 figure; references added, to appear in CQG(L)

We present a series of test beds for numerical codes designed to find apparent horizons. We consider three apparent horizon finders that use different numerical methods: one of them in axisymmetry, and two fully three-dimensional. We concentrate first on a toy model that has a simple horizon structure, and then go on to study single and multiple black hole data sets. We use our finders to look for apparent horizons in Brill wave initial data where we discover that some results published previously are not correct. For pure wave and multiple black hole spacetimes, we apply our finders to survey parameter space, mapping out properties of interesting data sets for future evolutions., Comment: 19 pages Revtex, 22 figures included

The Geroch-Wald-Jang-Huisken-Ilmanen approach to the positive energy problem to may be extended to give a negative lower bound for the mass of asymptotically Anti-de-Sitter spacetimes containing horizons with exotic topologies having ends or infinities of the form $\Sigma_g \times {\Bbb R}$, in terms of the cosmological constant. We also show how the method gives a lower bound for for the mass of time-symmetric initial data sets for black holes with vectors and scalars in terms of the mass, $|Z(Q,P)|$ of the double extreme black hole with the same charges. I also give a lower bound for the area of an apparent horizon, and hence a lower bound for the entropy in terms of the same function $|Z(Q,P)|$. This shows that the so-called attractor behaviour extends beyond the static spherically symmetric case. and underscores the general importance of the function $|Z(Q,P)|$. There are hints that higher dimensional generalizations may involve the Yamabe conjectures., Comment: 13pp. latex

The global structure of McVittie's solution representing a point mass embedded in a spatially flat Robertson-Walker universe is investigated. The scalar curvature singularity at proper radius R=2m, where m (constant) is the Schwarzschild mass, and the apparent horizon which surrounds it are studied. The conformal diagram for the spacetime is obtained via a qualitative analysis of the radial null geodesics. Particular attention is paid to the physical interpretation of this spacetime; previous work on this issue is reviewed, and to how recent quasi-local definitions of black and white holes relate to this spacetime.

This article investigates the interaction of a spherically symmetric massless scalar field with a strong gravitational field. It focuses on the propagation of waves in regions outside any horizons. The two factors acting on the waves can be identified as a redshift and a backscattering. The influence of backscattering on the intensity of the outgoing radiation is studied and rigorous quantitative upper bounds obtained. These show that the total flux may be decreased if the sources are placed in a region adjoining an apparent horizon. Backscattering can be neglected in the case $2m_0 /R<< 1$, that is when the emitter is located at a distance from a black hole much larger than the Schwarzschild radius. This backscattering may have noticeable astrophysical consequences., Revtex, 16 pages, 3 figures

In this paper we analyse the stability of black hole Cauchy horizons arising in a class of two-dimensional dilaton gravity theories that describes `accelerated' black holes. It is shown that, due to the characteristic asymptotic Rindler form of the metric or to the presence of an acceleration horizon, time-dependent gravitational perturbations generated in the external region do not necessarily blow up when propagated along the Cauchy horizon. There exists, in fact, a region of non-zero measure in the space of the parameters characterizing the solutions such that mass inflation is avoided and the spacetime geometry remains regular on this surface. Despite this fact, however, quantum backreaction seems to produce a scalar curvature singularity there.

Some one-parameter families of time-symmetric Cauchy hypersurfaces were investigated. All of them have such a property that for some `critical' value of the parameter an apparent horizon appears. It turns out that for parameter values sufficiently close to the critical one, numerous properties of the horizon are `universa' (i.e. independent of details of geometry and distribution of matter). It was conjectured that the above `universality' property occurs in the case of typical one-parameter time-symmetric families of Cauchy hypersurfaces.

We search for apparent horizons in various kinds of analytic initial data with axisymmetry but which allow some extreme matter configurations, in order to gain some insights into the hoop conjecture proposed by Thorne. The problem of defining the circumference C of a body is also considered, and a precise definition of C is proposed. For the models considered, the necessary condition for the apparent horizon formation is found to be where M is the ADM mass. Although initial data investigated here are only of a restricted class, it is interesting to note that this criterion almost coincides with the result obtained by Barrabes et al and by Tod who investiged a convex null dust shell.

The Cauchy horizon instability in the Reissner-Nordstrom solution is investigated numerically using (2+2) formalism. The formalism is based on the metric decomposition along two null coordinates parallel to the black hole horizons. The authors show that a spacelike singularity forms to prevent an observer's reaching the Cauchy horizon and the properties of the singularity are discussed in detail. They found that if the mass of the perturbation is of an order of or greater than the mass of the initial Reissner-Nordstrom black hole, the position of the singularity tends to those in the Schwarzschild solution. They also present a highly reliable numerical scheme based on the (2+2) formalism and discuss the properties of the initial value equations which in (2+2) formalism are reduced to linear equations.

The global structure of 2-dimensional dilaton gravity is studied, attending in particular to black holes and singularities. A gravitational energy is defined and shown to be positive at spatial singularities and negative at temporal singularities. Trapped points are defined, and it is shown that spatial singularities are trapped and temporal singularities are not. Thus a local form of cosmic censorship holds for positive energy. In an analogue of gravitational collapse to a black hole, matter falling into an initially flat space creates a spatial curvature singularity which is cloaked in a spatial or null apparent horizon with non-decreasing energy and area.

The solutions of the Dirac equation near the black hole event horizon and the universe horizon in the Vaidya-Schwarzschild-de Sitter space-time are given in this paper. Both the temperature of the Hawking radiation and the location of the evaporating black hole horizon and the universe horizon are determined exactly.

We improve the brick-wall model to take only the contribution of a thin film near the event horizon into account. This improvement not only gives us a satisfactory result, but also avoids some drawbacks in the original brick-wall method such as the little mass approximation, neglecting logarithm term, and taking the term L3 as the contribution of the vacuum surrounding a black hole. It is found that there is an intrinsic relation between the event horizon and the entropy. The event horizon is the characteristic of a black hole, so the entropy calculating of a black hole is also naturally related to its horizon.

The authors considers a time-symmetric, conformally flat and axisymmetric Cauchy hypersurface Sigma . It is assumed that the distribution of matter present in Sigma is strongly elongated in the direction of the symmetry axis and has compact support. Let L denote the length of this configuration as measured in the flat background space, and M the ADM mass associated with Sigma . It is shown that if the ratio M/L is sufficiently small, then such a configuration of matter cannot be entirely surrounded by an apparent horizon. The proof makes use of the second variation formula. Moreover, if the Penrose inequality is true, one can obtain more quantitative estimation of this ratio: if M

The stability of the Cauchy horizon in a Reissner-Nordstrom-de Sitter spacetime is examined via a perturbation analysis taking the generic initial condition of finite but non-zero influx as measured by an observer at the cosmological horizon.

The radiative tail of gravitational and electromagnetic perturbations accumulates at the Cauchy horizon of a Reissner-Nordstrom black hole, producing an instability of that horizon. This instability is usually interpreted as an infinite proper-time compression effect: a free-falling observer crossing the Cauchy horizon sees an infinite number of waves within a finite proper time, hence measuring infinite energy densities. The authors show, using a simple model in which a Reissner-Nordstrom black hole immersed in de Sitter space is perturbed by a radial stream of infalling light-like particles, that proper-time compression, though sufficient, is not a necessary condition for the instability of the Cauchy horizon is unstable whenever the surface gravity of the Cauchy horizon is greater than that of the cosmological horizon, in spite of the fact that there is no corresponding infinite proper-time compression.

It is proposed that the luminosity, the information and the frequency of a freely falling light source to an event horizon appear to the observer resting with respect to the horizon to decrease exponentially with a time scale which depends on the temperature of the horizon. This conclusion is valid not only for the Schwarzschild black hole, but also for the other black holes, the Rindler horizon, and the deSitter horizon.

Equilibrium thermodynamic laws are typically applied to horizons in general relativity without stating the conditions that bring them into equilibrium. We fill this gap by applying a new thermodynamic interpretation to a generalized Raychaudhuri equation for a worldsheet orthogonal to a closed spacelike 2-surface, the "screen", which encompasses a system of arbitrary size in nonequilibrium with its surroundings in general. In the case of spherical symmetry this enables us to identify quasilocal thermodynamic potentials directly related to standard quasilocal energy definitions. Quasilocal thermodynamic equilibrium is defined by minimizing the mean extrinsic curvature of the screen. Moreover, without any direct reference to surface gravity, we find that the system comes into quasilocal thermodynamic equilibrium when the screen is located at a generalized apparent horizon. Examples of the Schwarzschild, Friedmann-Lema\^itre and Lema\^itre-Tolman geometries are investigated and compared. Conditions for the quasilocal thermodynamic and hydrodynamic equilibrium states to coincide are also discussed, and a quasilocal virial relation is suggested as a potential application of this approach., Comment: 27 pages. v2 small typos fixed, matches published version

Black hole apparent horizons possess a natural notion of stability, whose spectral characterization can be related to the problem of the stationary quantum charged particle. Such mathematical relation leads to an "analyticity conjecture" on the dependence of the spectral properties on a complex "fine-structure-constant" parameter, that can reduce the study of the spectrum of the (non-selfadjoint) MOTS-stability operator to that of the (selfadjoint) Hamiltonian of the quantum charged particle. Moreover, this perspective might open an avenue to the spinorial treatment of apparent horizon (MOTS-)stability and to the introduction of semiclassical tools to explore some of the qualitative aspects of this black hole spectral problem., 6 pages, no figures, contribution to the proceedings volume of the Spanish Relativity Meeting ERE2014: "Almost 100 years after Einstein Revolution", Valencia, Spain, 1-5 September 2014

We consider a novel kind of plot for presenting the behaviour of null geodesics in Schwarzschild spacetime. Our diagram depicts various features of the light rays as recorded by different classes of observers. The idea stems from the use of phase portraits for illustrating the null geodesics in Schwarzschild spacetime, above and below the horizon of a black hole, but they reveal unphysical characteristics. The plots we propose are free from such anomalies. Moreover they allow us to discover new under-horizon features.

Motivated by the geometrical interpretation of Brans-Dicke (BD) scalar field which may also act as a torsion potential in Lyra geometry, we study the effects of spacetime torsion on the dynamics of a collapsing massive star. Taking the interior spacetime as the FLRW metric and the matter content as spherically symmetric, homogeneous perfect fluid with the equation of state (EoS) $p=w\rho$, we show that the collapse ends in a spacetime singularity which is of the strong curvature type in the sense of Tipler. Whether the trapped surfaces form during the dynamical evolution of the collapse depends on the torsion parameter, related to the BD coupling parameter, and the EoS subject to the conditions on physical reasonableness of the collapse configuration. Hence, the space of torsion and EoS parameters is divided into two portions, one for which the collapse process leads to the formation of apparent horizon and the other for which the apparent horizon is failed to form in the interior region. The nature of the singularity is examined from the exterior perspective, by searching for the existence of radial null geodesics reaching the faraway observers. Moreover, it is found that the effects of a dynamical torsion can be transferred to the outside region of the collapsing star, making the exterior region dynamic.

In this article we further develop the solution theory for the Einstein constraint equations on an n-dimensional, asymptotically Euclidean manifold M with interior boundary S. Building on recent results for both the asymptotically Euclidean and compact with boundary settings, we show existence of far-from-CMC and near-CMC solutions to the conformal formulation of the Einstein constraints when nonlinear Robin boundary conditions are imposed on S, similar to those analyzed previously by Dain (2004), by Maxwell (2004, 2005), and by Holst and Tsogtgerel (2013) as a model of black holes in various CMC settings, and by Holst, Meier, and Tsogtgerel (2013) in the setting of far-from-CMC solutions on compact manifolds with boundary. These "marginally trapped surface" Robin conditions ensure that the expansion scalars along null geodesics perpendicular to the boundary region S are non-positive, which is considered the correct mathematical model for black holes in the context of the Einstein constraint equations. Assuming a suitable form of weak cosmic censorship, the results presented in this article guarantee the existence of initial data that will evolve into a space-time containing an arbitrary number of black holes. A particularly important feature of our results are the minimal restrictions we place on the mean curvature, giving both near- and far-from-CMC results that are new., Comment: 25 pages, no figures

With a new method calculating the location and temperature of the event horizon of the non-static black hole, the Dirac equation is reduced and solved near the horizon in Vaidya space-time when the tortoise coordinate is adopted. The location of Vaidya event horizon, the Hawking temperature and the formula of thermal spectrum of the Dirac particles are derived.

In this paper we have considered holographic dark energy and studied its cosmology and thermodynamics. We have analyzed the generalized second law (GSL) of thermodynamics in a flat universe consisting of interacting dark energy and dark matter. We performed the analysis under both thermal equilibrium and nonequilibrium conditions. If the apparent horizon is taken as the boundary of the universe, we have shown that the rate of change of the total entropy of the universe is proportional to which in fact shows that the GSL is valid at the apparent horizon, irrespective of the sign of the deceleration parameter, . Hence, for any form of dark energy, the apparent horizon can be considered as a perfect thermodynamic boundary of the universe. We confirmed this conclusion by using the holographic dark energy model. When the event horizon is taken as the boundary, we found that the GSL is only partially satisfied. The analysis under nonequilibrium conditions revealed that the GSL is satisfied if the temperature of the dark energy is greater than the temperature of the dark matter.

We have briefly summarized three aspects of connections between gravitational dynamics and thermodynamics by focusing on three kinds of spacetime horizon: Causal Rindler horizon of spacetime, black hole event horizon, and apparent horizon in a Friedmann-Robertson-Walker (FRW) universe. For the causal Rindler horizon, we have derived the Einstein's field equations from the Clausius relation. For black hole horizon in a static spherically symmetric spacetime, we have shown that at the black hole horizon, the Einstein's field equations can be cast to a form of the first law of thermodynamics. Applying to the Clausius relation to apparent horizon of a FRW universe, one is able to derive the Friedmann equations, not only in Einstein gravity, but also in Lovelock gravity. We have shown that there exists Hawking radiation associated with the apparent horizon in the FRW universe.

The mass inflation phenomenon implies that black hole interiors are unstable due to a back-reaction divergence of the perturbed black hole mass function at the Cauchy horizon. Weak point in the standard mass inflation calculations is in a fallacious using of the global Cauchy horizon as a place for the maximal growth of the back-reaction perturbations instead of the local inner apparent horizon. It is derived the new spherically symmetric back-reaction solution for two counter-streaming light-like fluxes near the inner apparent horizon of the charged black hole by taking into account its separation from the Cauchy horizon. In this solution the back-reaction perturbations of the background metric are truly the largest at the inner apparent horizon, but, nevertheless, remain small. The back reaction, additionally, removes the infinite blue-shift singularity at the inner apparent horizon and at the Cauchy horizon., Comment: 14 pages, 2 figures, Fig. 1 is proofed

We show that one can always derive the Friedmann equation of an (n + 1)-dimensional Friedmann - Robertson - Walker universe in cubic quasi-topological gravity, by determining the difference between the bulk and the apparent horizon degrees of freedom in a region of space. We also generalize the study to the higher-order quasi-topological gravity, and extract the corresponding Friedmann equation in this theory by using the same approach. © 2014 Chinese Physical Society and IOP Publishing Ltd.

We investigate some cosmological features of the LCDM model in the framework of the generalized teleparallel theory of gravity f(T) where T denotes the torsion scalar. Its reconstruction is performed giving rise to an integration constant Q and other input parameters according to which we point out more analysis. Thereby, we show that for some values of this constant, the first and second laws of thermodynamics can be realized in the equilibrium description, for the universe with the temperature inside the horizon equal to that at the apparent horizon. Moreover, still within these suitable values of the constant, we show that the model may be stable using the de Sitter and Power-Law cosmological solutions., 25 pages, 2 figures, Accepted for publication in Journal of Cosmology and Astroparticle Physics (JCAP)

We study first and second laws of black hole thermodynamics at the apparent horizon of FRW spacetime in f(R,T,RμνTμν) gravity, where R, Rμν are the Ricci scalar and Riemann tensor and T is the trace of the energy-momentum tensor Tμν. We develop the Friedmann equations for any spatial curvature in this modified theory and show that these equations can be transformed to the form of Clausius relation ThSeff = δ. Here Th is the horizon temperature, Seff is the entropy which contains contributions both from horizon entropy and additional entropy term introduced due to the non-equilibrating description and δ is the energy flux across the horizon. The generalized second law of thermodynamics is also established in a more comprehensive form and one can recover the corresponding results in Einstein, f(R) and f(R,T) gravities. We discuss GSLT in the locality of assumption that temperature of matter inside the horizon is similar to that of horizon. Finally, we consider particular models in this theory and generate constraints on the coupling parameter for the validity of GSLT.

In recent several years, some works have been done on cosmic thermodynamics. The apparent horizon was regarded as the key characteristic supersurface where thermodynamics can be built on perfectly. However, if the irreversible process is considered, the proper position for building thermodynamics will not be the apparent horizon anymore. The new position is related to dark energy state equation and the irreversible process parameters.

Pop III stars are the first stars in the universe. They do not contain metals and their formation and evolution may be different from that of stars of later generations. In fact, according to the theory of star formation, Pop III stars might have very massive components ($\sim 100 - 10000M_\odot$). In this paper, we compute the spherically symmetric gravitational collapse of these Pop III massive stars. We solve the general relativistic hydrodynamics and neutrino transfer equations simultaneously, treating neutrino reactions in detail. Unlike supermassive stars ($\gtrsim 10^5 M_\odot$), the stars of concern in this paper become opaque to neutrinos. The collapse is simulated until after an apparent horizon is formed. We confirm that the neutrino transfer plays a crucial role in the dynamics of gravitational collapse, and find also that the $\beta$-equilibration leads to a somewhat unfamiliar evolution of electron fraction. Contrary to the naive expectation, the neutrino spectrum does not become harder for more massive stars. This is mainly because the neutrino cooling is more efficient and the outer core is more massive as the stellar mass increases. Here the outer core is the outer part of the iron core falling supersonically. We also evaluate the flux of relic neutrino from Pop III massive stars. As expected, the detection of these neutrinos is difficult for the currently operating detectors. However, if ever observed, the spectrum will enable us to obtain the information on the formation history of Pop III stars. We investigate 18 models covering the mass range of $300 - 10^4 M_\odot$, making this study the most detailed numerical exploration of spherical gravitational collapse of Pop III massive stars. This will also serve as an important foundation for multi-dimensional investigations., Comment: 32 pages, 11 figs, submitted to ApJ

Using a new tortoise coordinate transformation, we discuss the quantum nonthermal radiation characteristics near an event horizon by studying the Hamilton-Jacobi equation of a scalar particle in curved space-time, and obtain the event horizon surface gravity and the Hawking temperature on that event horizon. The results show that there is a crossing of particle energy near the event horizon. We derive the maximum overlap of the positive and negative energy levels. It is also found that the Hawking temperature of a black hole depends not only on the time, but also on the angle. There is a problem of dimension in the usual tortoise coordinate, so the present results obtained by using a correct-dimension new tortoise coordinate transformation may be more reasonable.

We investigate the generalized second law (GSL) of thermodynamics in the framework of $f(R)$-gravity. We consider a FRW universe filled only with ordinary matter enclosed by the dynamical apparent horizon with the Hawking temperature. For a viable modified gravity model as $f(R)=R-\alpha/R+\beta R^{2}$, we examine the validity of the GSL during the early inflation and late acceleration eras. Our results show that for the selected $f(R)$-gravity model minimally coupled with matter, the GSL in the early inflation epoch is satisfied only for the special range of the equation of state parameter of the matter. But in the late acceleration regime, the GSL is always respected., Comment: 10 pages, accepted by Europhys. Lett. 2012

A non-equilibrium picture of thermodynamics is discussed at the apparent horizon of FRW universe in $f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of the energy-momentum tensor. We take two forms of the energy-momentum tensor of dark components and demonstrate that equilibrium description of thermodynamics is not achievable in both cases. We check the validity of the first and second law of thermodynamics in this scenario. It is shown that the Friedmann equations can be expressed in the form of first law of thermodynamics $T_hdS'_h+T_hd_{\jmath}S'=-dE'+W'dV$, where $d_{\jmath}S'$ is the entropy production term. Finally, we conclude that the second law of thermodynamics holds both in phantom and non-phantom phases.

With appropriately chosen parameters, there exist the black-hole horizon and the cosmological horizon in the higher-dimensional Kerr-de Sitter spacetime, where these two horizons generally have different Hawking temperatures. In this letter we first reduce the higher-dimensional Kerr-de Sitter spacetime line element to a 2-dimensional one (the (t−r) sector) using the dimensional reduction method near the cosmological horizon, and then investigate the Unruh/Hawking effects of the cosmological horizon by the global embedding approach.

We study responses of the Brans-Dicke field due to gravitational collapses of scalar field pulses using numerical simulations. Double-null formalism is employed to implement the numerical simulations. If we supply a scalar field pulse, it will asymptotically form a black hole via dynamical interactions of the Brans-Dicke field. Hence, we can observe the responses of the Brans-Dicke field by two different regions. First, we observe the late time behaviors after the gravitational collapse, which include formations of a singularity and an apparent horizon. Second, we observe the fully dynamical behaviors during the gravitational collapse and view the energy-momentum tensor components. For the late time behaviors, if the Brans-Dicke coupling is greater (or smaller) than -1.5, the Brans-Dicke field decreases (or increases) during the gravitational collapse. Since the Brans-Dicke field should be relaxed to the asymptotic value with the elapse of time, the final apparent horizon becomes time-like (or space-like). For the dynamical behaviors, we observed the energy-momentum tensors around $\omega$ ~ -1.5. If the Brans-Dicke coupling is greater than -1.5, the $T_{uu}$ component can be negative at the outside of the black hole. This can allow an instantaneous inflating region during the gravitational collapse. If the Brans-Dicke coupling is less than -1.5, the oscillation of the $T_{vv}$ component allows the apparent horizon to shrink. This allows a combination that violates weak cosmic censorship. Finally, we discuss the implications of the violation of the null energy condition and weak cosmic censorship., Comment: 28 pages, 14 figures

We calculate the work made out by the apparent horizon (AH) of the Friedmann–Robertson–Walker (FRW) universe and the heat flux through the AH from the first law of thermodynamics. We discuss the mechanical properties of the AH and analyze the universe model for which the mechanical properties can change. Finally, the thermal properties of the AH of FRW universe are discussed.