Showing papers on "Black hole thermodynamics published in 2010"
Book•
25 May 2010
TL;DR: In this article, the physics of black holes are explored in terms of a membrane paradigm which treats the event horizon as a two-dimensional membrane embedded in three-dimensional space, and a 3+1 formalism is used to split Schwarzschild space-time and the laws of physics outside a nonrotating hole.
Abstract: The physics of black holes is explored in terms of a membrane paradigm which treats the event horizon as a two-dimensional membrane embedded in three-dimensional space. A 3+1 formalism is used to split Schwarzschild space-time and the laws of physics outside a nonrotating hole, which permits treatment of the atmosphere in terms of the physical properties of thin slices. The model is applied to perturbed slowly or rapidly rotating and nonrotating holes, and to quantify the electric and magnetic fields and eddy currents passing through a membrane surface which represents a stretched horizon. Features of tidal gravitational fields in the vicinity of the horizon, quasars and active galalctic nuclei, the alignment of jets perpendicular to accretion disks, and the effects of black holes at the center of ellipsoidal star clusters are investigated. Attention is also given to a black hole in a binary system and the interactions of black holes with matter that is either near or very far from the event horizon. Finally, a statistical mechanics treatment is used to derive a second law of thermodynamics for a perfectly thermal atmosphere of a black hole.
913 citations
TL;DR: In this paper, the authors provide a physical interpretation for the field equations of gravity based on a thermodynamic perspective, and the virtual degrees of freedom associated with the horizons, as perceived by the local Rindler observer, play a crucial role in this approach.
Abstract: It is possible to provide a physical interpretation for the field equations of gravity based on a thermodynamical perspective. The virtual degrees of freedom associated with the horizons, as perceived by the local Rindler observer, play a crucial role in this approach. In this context, the relation S = E/2T between the entropy (S), active gravitational mass (E) and temperature (T) — obtained previously in gr-qc/0308070 [CQG, 21, 4485 (2004)] — can be reinterpreted as the law of equipartition E = (1/2) nkBT where $n=\Delta A/L_{\rm P}^2$ is the number (density) of microscopic horizon degrees of freedom in an area ΔA. Conversely, one can use the equipartition argument to provide a thermodynamic interpretation of gravity, even in the nonrelativistic limit. These results emphasize the intrinsic quantum nature of all gravitational phenomena and diminishes the distinction between thermal phenomena associated with local Rindler horizons and the usual thermodynamics of macroscopic bodies in non-inertial frames. J...
348 citations
TL;DR: In this paper, the authors constructed the first supersymmetric black holes in AdS4 with nonconstant scalar fields and showed that the black hole entropy depends only on the charges, in agreement with the attractor mechanism.
Abstract: Using the general recipe given in arXiv:0804.0009, where all timelike supersymmetric solutions of $ \mathcal{N} = 2 $
, D = 4 gauged supergravity coupled to abelian vector multiplets were classified, we construct the first examples of genuine supersymmetric black holes in AdS4 with nonconstant scalar fields. This is done for various choices of the prepotential, amongst others for the STU model. These solutions permit to study the BPS attractor flow in AdS. We also determine the most general supersymmetric static near-horizon geometry and obtain the attractor equations in gauged supergravity. As a general feature we find the presence of flat directions in the black hole potential, i.e., generically the values of the moduli on the horizon are not completely specified by the charges. For one of the considered prepotentials, the resulting moduli space is determined explicitely. Still, in all cases, we find that the black hole entropy depends only on the charges, in agreement with the attractor mechanism.
314 citations
TL;DR: In this article, the authors developed and significantly generalized the effective world volume theory for higher-dimensional black holes, which regards the black hole as a black brane curved into a submanifold of a background spacetime.
Abstract: We develop and significantly generalize the effective worldvolume theory for higher-dimensional black holes recently proposed by the authors. The theory, which regards the black hole as a black brane curved into a submanifold of a background spacetime — a blackfold—, can be formulated in terms of an effective fluid that lives on a dynamical worldvolume. Thus the blackfold equations split into intrinsic (fluid-dynamical) equations, and extrinsic (generalized geodesic embedding) equations. The intrinsic equations can be easily solved for equilibrium configurations, thus providing an efficient formalism for the approximate construction of novel stationary black holes. Furthermore, it is possible to study time evolution. In particular, the long-wavelength component of the Gregory-Laflamme instability of black branes is obtained as a sound-mode instability of the effective fluid. We also discuss action principles, connections to black hole thermodynamics, and other consequences and possible extensions of the approach. Finally, we outline how the fluid/AdS-gravity correspondence is related to this formalism.
270 citations
TL;DR: In this article, a new gravitational action which includes cubic curvature interactions and which provides a useful toy model for the holographic study of a three parameter family of four-and higher-dimensional CFTs was constructed.
Abstract: We construct a new gravitational action which includes cubic curvature interactions and which provides a useful toy model for the holographic study of a three parameter family of four- and higher-dimensional CFT’s We also investigate the black hole solutions of this new gravity theory Further we examine the equations of motion of quasi-topological gravity While the full equations in a general background are fourth-order in derivatives, we show that the linearized equations describing gravitons propagating in the AdS vacua match precisely the second-order equations of Einstein gravity
255 citations
TL;DR: In this article, a cubic theory of gravity in five dimensions with second-order traced field equations is presented, analogous to BHT new massive gravity in three dimensions, which admits a new asymptotically locally flat black hole.
Abstract: We present a new cubic theory of gravity in five dimensions which has second-order traced field equations, analogous to BHT new massive gravity in three dimensions. Moreover, for static spherically symmetric spacetimes all the field equations are of second order, and the theory admits a new asymptotically locally flat black hole. Furthermore, we prove the uniqueness of this solution, study its thermodynamical properties and show the existence of a C-function for the theory following the arguments of Anber and Kastor (2008 J. High Energy Phys. JHEP05(2008)061 (arXiv:0802.1290 [hep-th])) in pure Lovelock theories. Finally, we include the Einstein–Gauss–Bonnet and cosmological terms and find new asymptotically AdS black holes at the point where the three maximally symmetric solutions of the theory coincide. These black holes may also possess a Cauchy horizon.
224 citations
TL;DR: This work shows that this boundary condition given on a null surface representing the event horizon can be treated in a manifestly SU(2) invariant manner and settles previous controversies concerning the counting of states.
Abstract: Black holes (BH's) in equilibrium can be defined locally in terms of the so-called isolated horizon boundary condition given on a null surface representing the event horizon. We show that this boundary condition can be treated in a manifestly SU(2) invariant manner. Upon quantization, state counting is expressed in terms of the dimension of Chern-Simons Hilbert spaces on a sphere with punctures. Remarkably, when considering an ensemble of fixed horizon area a(H), the counting can be mapped to simply counting the number of SU(2) intertwiners compatible with the spins labeling the punctures. The resulting BH entropy is proportional to a(H) with logarithmic corrections ΔS=-3/2 loga(H). Our treatment from first principles settles previous controversies concerning the counting of states.
207 citations
TL;DR: In this paper, the authors complete the program of noncomutative geometry inspired black holes, providing the richest possible solution, endowed with mass, charge and angular momentum, and provide a prescription for employing the Newman-Janis algorithm in the case of nonvanishing stress tensors, finding regular axisymmetric charged black holes in the presence of a minimal length.
Abstract: In this paper we complete the program of the noncomutative geometry inspired black holes, providing the richest possible solution, endowed with mass, charge and angular momentum. After providing a prescription for employing the Newman-Janis algorithm in the case of nonvanishing stress tensors, we find regular axisymmetric charged black holes in the presence of a minimal length. We study also the new thermodynamics and we determine the corresponding higher-dimensional solutions. As a conclusion we make some consideration about possible applications.
206 citations
TL;DR: In this paper, a detailed analysis of the spherically symmetric isolated horizon system is performed in terms of the connection formulation of general relativity, and the system is shown to admit a manifestly SU(2) invariant formulation where the effective horizon degrees of freedom are described by an SU (2) Chern-Simons theory.
Abstract: A detailed analysis of the spherically symmetric isolated horizon system is performed in terms of the connection formulation of general relativity. The system is shown to admit a manifestly SU(2) invariant formulation where the (effective) horizon degrees of freedom are described by an SU(2) Chern-Simons theory. This leads to a more transparent description of the quantum theory in the context of loop quantum gravity and modifications of the form of the horizon entropy.
192 citations
TL;DR: In this article, the authors construct asymptotically AdS5 solutions to 5-dimensional Einstein-Maxwell theory with Chern-Simons term which are dual to 4-dimensional gauge theories, including $$\mathcal{N} = 4 $$ SYM theory, in the presence of a constant background magnetic field B and a uniform electric charge density ρ.
Abstract: We construct asymptotically AdS5 solutions to 5-dimensional Einstein-Maxwell theory with Chern-Simons term which are dual to 4-dimensional gauge theories, including $$\mathcal{N} = 4 $$
SYM theory, in the presence of a constant background magnetic field B and a uniform electric charge density ρ. For the solutions corresponding to supersymmetric gauge theories, we find numerically that a small magnetic field causes a drastic decrease in the entropy at low temperatures. The near-horizon AdS2 × R
3 geometry of the purely electrically charged brane thus appears to be unstable under the addition of a small magnetic field. Based on this observation, we propose a formulation of the third law of thermodynamics (or Nernst theorem) that can be applied to black holes in the AdS/CFT context. We also find interesting behavior for smaller, non-supersymmetric, values of the Chern-Simons coupling k. For k = 1 we exhibit exact solutions corresponding to warped AdS3 black holes, and show that these can be connected to asymptotically AdS5 spacetime. For k ≤ 1 the entropy appears to go to a finite value at extremality, but the solutions still exhibit a mild singularity at strictly zero temperature. In addition to our numerics, we carry out a complete perturbative analysis valid to order B
2, and find that this corroborates our numerical results insofar as they overlap.
179 citations
TL;DR: In this article, it was shown that a general parity preserving theory of gravity in 2+1 dimensions involving upto four derivative curvature invariants reduces to the new massive gravity theory.
Abstract: Demanding the existence of a simple holographic c-theorem, it is shown that a general (parity preserving) theory of gravity in 2+1 dimensions involving upto four derivative curvature invariants reduces to the new massive gravity theory. We consider extending the theory including upto six derivative curvature invariants. Black hole solutions are presented and consistency with 1+1 CFTs is checked. We present evidence that bulk unitarity is still in conflict with a positive CFT central charge for generic choice of parameters.
TL;DR: In this article, a more general relation between the energy density and the radial pressure was considered and new geometries describing a regular "dirty black hole" was proposed. But the relation between energy density, radial pressure and the energy condition violation was not considered.
Abstract: We provide a new exact solution of the Einstein equations which generalize the noncommutative geometry-inspired Schwarzschild metric, we previously obtained. We consider here a more general relation between the energy density and the radial pressure and find new geometries describing a regular 'dirty black hole'. We discuss strong and weak energy condition violation and various aspects of the regular dirty black hole thermodynamics.
TL;DR: In this paper, it was shown that the near horizon limit of the extremal BTZ black hole is a self-dual orbifold of AdS3 with a null circle on its boundary, and thus the dual field theory is a Discrete Light Cone Quantized (DLCQ) two dimensional CFT.
Abstract: The near horizon limit of the extremal BTZ black hole is a "self-dual orbifold" of AdS3. This geometry has a null circle on its boundary, and thus the dual field theory is a Discrete Light Cone Quantized (DLCQ) two dimensional CFT. The same geometry can be compactified to two dimensions giving AdS2 with a constant electric field. The kinematics of the DLCQ show that in a consistent quantum theory of gravity in these backgrounds there can be no dynamics in AdS2, which is consistent with older ideas about instabilities in this space. We show how the necessary boundary conditions eliminating AdS2 fluctuations can be implemented, leaving one copy of a Virasoro algebra as the asymptotic symmetry group. Our considerations clarify some aspects of the chiral CFTs appearing in proposed dual descriptions of the near-horizon degrees of freedom of extremal black holes.
TL;DR: Banerjee and Majhi as discussed by the authors derived the spectrum of entropy/area of a perfect black body using the first law of black hole thermodynamics and showed that the entropy is not proportional to the horizon area of the black hole.
TL;DR: In this paper, a class of exact analytic and static, spherically symmetric black hole solutions in the semi-classical Einstein equations with Weyl anomaly with Wey anomaly was presented.
Abstract: We present a class of exact analytic and static, spherically symmetric black hole solutions in the semi-classical Einstein equations with Weyl anomaly. The solutions have two branches, one is asymptotically flat and the other asymptotically de Sitter. We study thermodynamic properties of the black hole solutions and find that there exists a logarithmic correction to the well-known Bekenstein-Hawking area entropy. The logarithmic term might come from non-local terms in the effective action of gravity theories. The appearance of the logarithmic term in the gravity side is quite important in the sense that with this term one is able to compare black hole entropy up to the subleading order, in the gravity side and in the microscopic statistical interpretation side.
TL;DR: In this paper, the relationship between the first law of thermodynamics and the gravitational field equation at a static, spherically symmetric black hole horizon in Horava-Lifshitz theory with/without detailed balance was explored.
Abstract: We explore the relationship between the first law of thermodynamics and gravitational field equation at a static, spherically symmetric black hole horizon in Horava-Lifshitz theory with/without detailed balance. It turns out that as in the cases of Einstein gravity and Lovelock gravity, the gravitational field equation can be cast to a form of the first law of thermodynamics at the black hole horizon. This way we obtain the expressions for entropy and mass in terms of black hole horizon, consistent with those from other approaches. We also define a generalized Misner-Sharp energy for static, spherically symmetric spacetimes in Horava-Lifshitz theory. The generalized Misner-Sharp energy is conserved in the case without matter field, and its variation gives the first law of black hole thermodynamics at the black hole horizon.
TL;DR: In this article, a systematic scan of the landscape of black holes in any spacetime dimension using the recently proposed blackfold effective worldvolume theory is performed. But the authors focus primarily on asymptotically flat stationary vacuum solutions, where they uncover large classes of new black holes.
Abstract: We initiate a systematic scan of the landscape of black holes in any spacetime dimension using the recently proposed blackfold effective worldvolume theory. We focus primarily on asymptotically flat stationary vacuum solutions, where we uncover large classes of new black holes. These include helical black strings and black rings, black odd-spheres, for which the horizon is a product of a large and a small sphere, and non-uniform black cylinders. More exotic possibilities are also outlined. The blackfold description recovers correctly the ultraspinning Myers-Perry black holes as ellipsoidal even-ball configurations where the velocity field approaches the speed of light at the boundary of the ball. Helical black ring solutions provide the first instance of asymptotically flat black holes in more than four dimensions with a single spatial U(1) isometry. They also imply infinite rational non-uniqueness in ultraspinning regimes, where they maximize the entropy among all stationary single-horizon solutions. Moreover, static blackfolds are possible with the geometry of minimal surfaces. The absence of compact embedded minimal surfaces in Euclidean space is consistent with the uniqueness theorem of static black holes.
TL;DR: In this article, the authors studied black holes in the Hořava-Lifshitz gravity with a parameter λ and derived the temperature, mass, entropy, and heat capacity for investigating thermodynamic properties of these black holes.
Abstract: We study black holes in the Hořava–Lifshitz gravity with a parameter λ. For 1/3≤λ 3, the black holes behave the Reissner–Nordstrom type black hole in asymptotically flat spacetimes. Hence, these all are quite different from the Schwarzschild–AdS black hole of Einstein gravity. The temperature, mass, entropy, and heat capacity are derived for investigating thermodynamic properties of these black holes.
TL;DR: In this paper, the Hartle-Hawking-like states of quantum field theories on asymptotically AdS black hole backgrounds were studied with particular regard to the phase structure of interacting theories.
Abstract: We study Hartle–Hawking-like states of quantum field theories on asymptotically AdS black hole backgrounds, with particular regard to the phase structure of interacting theories. By a suitable analytic continuation we show that the equilibrium dynamics of field theories on large asymptotically AdS black holes can be related to the low-temperature states of the same field theory on the AdS soliton (or pure AdS) background. This allows us to gain insight into Hartle–Hawking-like states on large-radius Schwarzschild- or rotating-AdS black holes. Furthermore, we exploit the AdS/CFT correspondence to explore the physics of strongly coupled large N theories on asymptotically AdS black holes. In particular, we exhibit a plausibly complete set of phases for the M2-brane world-volume superconformal field theory on a BTZ black hole background. Our analysis partially resolves puzzles previously raised in connection with Hawking radiation on large AdS black holes.
TL;DR: The entropy-area spectrum of a black hole has been a long-standing and unsolved problem as mentioned in this paper, and it has been shown that both entropy and area spectrum are evenly spaced.
TL;DR: In this paper, the authors obtained exact solutions of charged asymptotically Lifshitz black holes in arbitrary (d + 2) dimensions, generalizing the four dimensional solution investigated in 0908.2611[hep-th].
Abstract: We obtain exact solutions of charged asymptotically Lifshitz black holes in arbitrary (d + 2) dimensions, generalizing the four dimensional solution investigated in 0908.2611[hep-th]. We find that both the conventional Hamiltonian approach and the recently proposed method for defining mass in non-relativistic backgrounds do not work for this specific example. Thus the mass of the black hole can only be determined by the first law of thermodynamics. We also obtain perturbative solutions in five-dimensional Gauss-Bonnet gravity. The ratio of shear viscosity over entropy density and the DC conductivity are calculated in the presence of Gauss-Bonnet corrections.
TL;DR: In this paper, it was shown that the entropy of the non-extremal Reissner-Nordstrom black hole may be carried by the five-dimensional compactification solution with central charge c = 6 Q e 3.
TL;DR: This article derived a new generalised uncertainty principle (GUP) based on certain general assumptions and used it to study Schwarzschild black hole thermodynamics and found that the evaporation process stops at a particular mass, referred as the remnant mass.
TL;DR: In this paper, the phase transition of planar black holes in Horava-Lifshitz gravity was discussed by introducing a Maxwell field and a complex scalar field, and it was found that there exists a spike in the conductivity for the operator with scaling dimension one.
Abstract: We discuss the phase transition of planar black holes in Horava-Lifshitz gravity by introducing a Maxwell field and a complex scalar field. We calculate the condensate of the charged operators in the dual conformal field theories when the mass square of the complex scalar field is m(2) = -2/L(2) and m(2) = 0, respectively. We compute the electrical conductivity of the Horava-Lifshitz superconductor in the probe approximation. In particular, it is found that there exists a spike in the conductivity for the case of the operator with scaling dimension one. These results are quite similar to those in the case of Schwarzschild-AdS black holes, which demonstrates that the holographic superconductivity is a robust phenomenon associated with asymptotic AdS black holes.
TL;DR: In this article, the authors studied the non-equilibrium condensation process in a holographic superconductor and showed that the initial perturbations grow exponentially and, eventually, spacetimes approach the hairy black holes.
Abstract: We study the non-equilibrium condensation process in a holographic superconductor. When the temperature T is smaller than a critical temperature T
c
, there are two black hole solutions, the Reissner-Nordstrom-AdS black hole and a black hole with a scalar hair. In the boundary theory, they can be regarded as the supercooled normal phase and the superconducting phase, respectively. We consider perturbations on supercooled Reissner-Nordstrom-AdS black holes and study their non-linear time evolution to know about physical phenomena associated with rapidly-cooled superconductors. We find that, for T < T
c
, the initial perturbations grow exponentially and, eventually, spacetimes approach the hairy black holes. We also clarify how the relaxation process from a far-from-equilibrium state proceeds in the boundary theory by observing the time dependence of the superconducting order parameter. Finally, we study the time evolution of event and apparent horizons and discuss their correspondence with the entropy of the boundary theory. Our result gives a first step toward the holographic understanding of the non-equilibrium process in superconductors.
TL;DR: In this paper, it was shown that the entropy of a stationary black hole is proportional to the gravity action, and that the relation is also compatible with the generalized Smarr formula for mass.
Abstract: Starting from the definition of entropy used in statistical mechanics we show that it is proportional to the gravity action. For a stationary black hole this entropy is expressed as $S=E/2T$, where $T$ is the Hawking temperature and $E$ is shown to be the Komar energy. This relation is also compatible with the generalized Smarr formula for mass.
TL;DR: In this paper, the authors investigated the validity of the generalized second law of thermodynamics in a universe governed by Hořava-Lifshitz gravity and found that it is generally valid for flat and closed geometry and conditionally valid for an open universe, while beyond detailed balance it is only conditionally sufficient for all curvatures.
Abstract: We investigate the validity of the generalized second law of thermodynamics in a universe governed by Hořava-Lifshitz gravity. Under the equilibrium assumption, that is in the late-time cosmological regime, we calculate separately the entropy time-variation for the matter fluid and, using the modified entropy relation, that of the apparent horizon itself. We find that under detailed balance the generalized second law is generally valid for flat and closed geometry and it is conditionally valid for an open universe, while beyond detailed balance it is only conditionally valid for all curvatures. Furthermore, we also follow the effective approach showing that it can lead to misleading results. The non-complete validity of the generalized second law could either provide a suggestion for its different application, or act as an additional problematic feature of Hořava-Lifshitz gravity.
TL;DR: The ability to manipulate and understand the spectrum up to the level of detail that is described in the paper is a crucial step towards obtaining the behavior of entropy in the asymptotic (large horizon area) regime.
Abstract: We give a complete and detailed description of the computation of black hole entropy in loop quantum gravity by employing the most recently introduced number-theoretic and combinatorial methods. The use of these techniques allows us to perform a detailed analysis of the precise structure of the entropy spectrum for small black holes, showing some relevant features that were not discernible in previous computations. The ability to manipulate and understand the spectrum up to the level of detail that we describe in the paper is a crucial step toward obtaining the behavior of entropy in the asymptotic (large horizon area) regime.
TL;DR: In this paper, it was shown that near-extreme Reissner-Nordstrom-anti-de Sitter black holes are unstable against the condensation of an uncharged scalar field with mass close to the Breitenlohner-Freedman bound.
Abstract: Near-extreme Reissner-Nordstrom-anti-de Sitter black holes are unstable against the condensation of an uncharged scalar field with mass close to the Breitenlohner-Freedman bound. It is shown that a similar instability afflicts near-extreme large rotating AdS black holes, and near-extreme hyperbolic Schwarzschild-AdS black holes. The resulting nonlinear hairy black hole solutions are determined numerically. Some stability results for (possibly charged) scalar fields in black hole backgrounds are proved. For most of the extreme black holes we consider, these demonstrate stability if the “effective mass” respects the near-horizon BF bound. Small spherical Reissner-Nordstrom-AdS black holes are an interesting exception to this result.
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TL;DR: In this paper, the authors define an entropy which is purely geometrical for black holes and explain Wald's formulation which identifies black hole entropy for an arbitrary covariant theory of gravity, and distinguish thermodynamic laws which are kinematic from those which are dynamical.
Abstract: The laws of mechanics of stationary black holes bear a close resemblance with the laws of thermodynamics This is not only a mathematical analogy but also a physical one that helps us answer deep questions related to the thermodynamic properties of the black holes It turns out that we can define an entropy which is purely geometrical for black holes In this thesis we explain Wald's formulation which identifies black hole entropy for an arbitrary covariant theory of gravity We would like to know precisely what inputs go into arriving at Wald's formalism This expression for the entropy clearly depends on the precise form of the action The secondary theme of this thesis is to distinguish thermodynamic laws which are kinematic from those which are dynamical We would like to see explicitly in the derivation of these laws, where exactly the form of action plays a role In the beginning we motivate the definition of entropy using the Einstein-Hilbert Lagrangian We encounter the Zeroth law, the Hawking radiation, the second law, and then Wald's formulation