Black Hole Thermodynamics, Casimir Effect and Induced Gravity

An analogy between the subtraction procedure in the Gibbons-Hawking Euclidean path integral approach to black hole thermodynamics and the Casimir effect is shown. Then a conjecture about a possible Casimir nature of the Gibbons-Hawking subtraction is made in the framework of Sakharov's induced gravity. In this framework it appears that the degrees of freedom involved in the Bekenstein-Hawking entropy can be naturally identified with zero-point modes of the matter fields. Some consequences of this view are sketched.     

Quantum Black Hole

Creation of a black hole in quantum cosmology is the third way of black hole formation. In contrast to the gravitational collapse from a massive body in astrophysics or from the quantum fluctuation of matter fields in the very early universe, in the quantum cosmology scenario the black hole is essentially created from nothing. The black hole originates from a constrained gravitational instanton. The probability of creation for all kinds of single black holes in the Kerr-Newman family, at the semiclassical level, is the exponential of the total entropy of the universe, or one quarter of the sum of both the black hole and the cosmological horizon areas. The de Sitter spacetime is the most probable evolution at the Planckian era.     

Letter: Entropy Bound for a Charged Object from the Kerr-Newman Black Hole

We derive again the upper entropy bound for acharged object by employing thermodynamics of theKerr-Newman black hole linearised with respect to itselectric charge.     

Pure States Don't Wear Black

Recently, string theory has provided some remarkable new insights into the microphysics of black holes. I argue that a simple and important lesson is also provided with regards to the information loss paradox, namely, pure quantum states do not form black holes! Thus it seems black hole formation, as well as evaporation, must be understood within the framework of quantum decoherence.     

Towards a Probabilistic Paradigm for Gravitational Collapse, Black Hole Creation and Singularity Smearing

A prototype probability interpretation ispresented for the Oppenheimer-Snyder model ofspherically symmetric, gravitational collapse of apressureless ensemble of n point particles. A transitionprobability P(R(t), t; R₁, t₁) isderived for an initial sphere or fluid star of radius Rat comoving time t, collapsing smoothly andhomogeneously to any finite radii R(t, r) < R atcomoving t > t₁ and R(t) = 0 at t = t_f. The transitionprobability is evaluated in two cases. In the firstcase, Planck's constant is assumed zero and smoothdifferential limits exist for space and matter on alllength scales down to zero. The probability for singularityformation converges smoothly to unity as R 0 ort t_f: the collapse is deterministic atall scales. There is also a finite, nonzero probabilityof event horizon formation at R = R_h = 2GM, but the starcontinues to collapse through this radius since there isalways a higher probability of reaching any smallerradius R < R_h. An event horizon forms sothe collapsed state is still a black hole. In the classical limit(as 0) the singularity returns with unitprobability. Finally, we briefly discuss how the final,fuzzy, collapsed state may be related to aspects ofstring theory. The emphasis of the paper is on theconceptual ideas and general possibilities which couldarise when incorporating stochastic mechanics andanalysis into general relativistic collapse.     

Thermodynamic Classifications and Dilatonic Black Holes

We analyze the thermodynamics of systems which have entropy functions of the type S(m) = am + b, where m is an extensive variable and a, b, and are constants. Such functions apply to dilatonic black holes whose mass is m. This analysis continues our earlier treatment of the general classification of the thermodynamics of systems by whether they exhibit entropy functions which may or may not be either superadditive, homogeneous or concave in the extensive variables on which the entropy depends. This leads to a classification into 8 types of thermodynamics (with several subtypes). We show that only five of these are available for systems having the entropy given above, and these are in fact realized if the constants are given appropriate values.     

Perturbative Approach to the Inner Structure of a Rotating Black Hole

This is the first in a series of papers analyzing the inner structure of a generic rotating black hole. The black hole is assumed to evolve from the gravitational collapse of an isolated rotating object in an empty asymptotically-flat universe. This paper covers the first stages of the evolution: from the gravitational collapse and the formation of a black hole, up to the stage where the black hole settles down to Kerr. We shall discuss the generalization of Price's analysis (regarding the latetime asymptotic decay of perturbations outside the black hole) from Schwarzschild to Kerr, and present preliminary results. We then consider these external small perturbations as initial data for the evolution of perturbations inside the black hole. We demonstrate that an important region inside the black hole, which we call the late-time region (and which extends up to the inner horizon) experiences (arbitrarily) small initial perturbations. This, we argue, justifies the attempt to apply the small-perturbation approach to the black hole's interior. We discuss the physical significance of this late-time region. We shall also outline the strategy we use for evolving the perturbations from the event horizon to the inner horizon.     

LETTER: Pair Creation of Schwarzschild-anti-de Sitter Black Holes

For a spherically symmetric vacuum model with anegative cosmological constant, a complex constrainedinstanton is considered as the seed for the quantum paircreation of Schwarzschild-anti-de Sitter black holes. The relative creation probability isfound to be the exponential of the negative of the blackhole entropy. The black hole entropy is known to be onequarter of the black hole horizon area. In the absence of a general noboundary proposal foropen creation, the constrained instanton approach isused in treating both the open and closed pair creationsof black holes.     

The Quantum Corrections to the Entropy of Stationary Axisymmetric Einstein-Maxwell-Dilaton-Axion Black Holes

By using 't Hooft's brick wall model, thecorrections for a massless quantum scalar field to theblack hole entropy are studied in a stationaryaxisymmetric Einstein-Maxwell-dilaton-axion black holespace-time. The free energy and entropy for this case arecalculated; in Hartle-Hawking states, the derivedquantum entropy is composed of the part that has ageometric feature and the part that is logarithmically divergent, and it turns out that thelogarithmic part is related to the characteristicquantities of a black hole.     

Region of Magnetic Dominance near a Rotating Black Hole

Processes of collimation of electrically charged particles near a rotating black hole are discussed. It is assumed that the black hole is immersed in a weak magnetic field aligned with rotation axis. This situation is relevant for understanding pre-collimation of astrophysical jets. The magnetic field affects the motion of material and restricts the validity of various scenarios which use the test-particle (cold plasma) approximation. A simplified criterion to estimate the relevance of this approximation is discussed in connection with the mechanism of the dissipative collimation, as proposed by de Felice and Curir.     

Einstein-Fokker-Planck Equation for a Collapsing Perfect Fluid Star in a Thermal Noise Bath: Static Thermal Black Hole as the Equilibrium Solution

This paper considers sphericalOppenheimer-Snyder gravitational collapse of dust orperfect fluid stars immersed within aspacetime containing a thermal bath of (Gaussian) whitenoise at a temperature T, obeying the autocorrelations of thefluctation-dissipation theorem. Candidates for theresulting non-linear Einstein-Langevin (EL) stochasticdifferential field equations are developed. A collapsing fluid or dust star coupled to the stochastic,external thermal bath of fluctuations is theninterpreted as an example of a non-linear, noisy system,somewhat analogous to a non-linear Brownian motion in a viscous, thermal bath at temperature T. AnEinstein-Fokker-Planck (EFP) hydrodynamical continuityequation, describing the collapse as a probability flowwith respect to the exterior standard time t_s outside the collapsing body, is developed. Thethermal equilibrium or stationary solution can bederived in the infinite standard time relaxation limit.This limit (t_s ) only exists for a static, external observer within thenoise bath viewing the collapsing sphere such that R 1 (the event horizon) with unit probability ast_s . The stationary or thermalequilibrium solution of the efp equations therefore seemsto correspond to a static black hole in a Hartle-Hawkingstate at the Hawking temperature t_H. The OSmodel first predicted event horizons and singularities. It is interesting that through a simplestochastic extension of the model, one can conclude thatthe final collapsed, static, equilibrium state of thebody must be a thermal black hole at the Hawkingtemperature.     

Geodesic Motions in 2 + 1-Dimensional Charged Black Holes

We study the geodesic motions of a test particle around 2 + 1-dimensional charged black holes. We obtain a class of exact geodesic motions for the massless test particle when the ratio of its energy and angular momentum is given by the square root of the cosmological constant. The other geodesic motions for both massless and massive test particles are analyzed using the numerical method.     

Statistical Mechanics of a New Regular Black Hole

In this work we consider a new proposed regular black hole and study statistics of this black hole. We calculate partition function and related quantities which determine statistics of this black hole. We confirm that the microscopic entropy coincides with BH entropy.     

Quantum Statistical Entropy of Black Hole

By using the method of quantum statistics, we derive the partition function of bosonic and fermionic field in various coordinates and obtain the integral expression of the entropy of a black hole. Then via the improved brick-wall method, membrane model, we obtain that if we choose proper parameter, the entropy of black hole is proportional to the area of horizon. In our result, the stripped term and the divergent logarithmic term in the original brick-wall method no longer exist. We offer a new simple and direct way of calculating the entropy of black holes in various coordinates.     

Quantum Statistical Entropy of Five-Dimensional Black Hole

The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole. By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Further it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole's entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.     

From Schwarzschild to Kerr due to Black Hole Quantum Tunnelling

Hawking radiation can be viewed as a process of quantum tunnelling near black hole horizon. When a particle with angular momentum tunnels across the event horizon of Schwarzschild black hole, the black hole will change into a Kerr black hole. The emission rate of the massless particles with angular momentum is calculated, and the result is consistent with an underlying unitary theory.     

Quantum Statistical Entropy of Dielectric Black Hole

Using the new equation of state density from the generalized uncertainty principle in quantum gravity, we study statistical entropy of a dielectric black hole. When λ introduced in the generalized uncertainty principle takes a specific value, we find that the leading term of the statistical entropy of the dielectric black hole takes the Bekenstein-Hawking entropy form. In addition a finite correction term is also obtained. Comparing with the original brick-wall model, in our calculation there is no divergence and the small mass approximation is also not needed.     

Interior of a Schwarzschild Black Hole Revisited

The Schwarzschild solution has played a fundamental conceptual role in general relativity, and beyond, for instance, regarding event horizons, spacetime singularities and aspects of quantum field theory in curved spacetimes. However, one still encounters the existence of misconceptions and a certain ambiguity inherent in the Schwarzschild solution in the literature. By taking into account the point of view of an observer in the interior of the event horizon, one verifies that new conceptual difficulties arise. In this work, besides providing a very brief pedagogical review, we further analyze the interior Schwarzschild black hole solution. Firstly, by deducing the interior metric by considering time-dependent metric coefficients, the interior region is analyzed without the prejudices inherited from the exterior geometry. We also pay close attention to several respective cosmological interpretations, and briefly address some of the difficulties associated to spacetime singularities. Secondly, we deduce the conserved quantities of null and timelike geodesics, and discuss several particular cases in some detail. Thirdly, we examine the Eddington–Finkelstein and Kruskal coordinates directly from the interior solution. In concluding, it is important to emphasize that the interior structure of realistic black holes has not been satisfactorily determined, and is still open to considerable debate.     

Schwarzschild Black Hole as a Particle Accelerator

JETP Letters - We consider collision of two particles near the horizon of a nonextremal static black hole. At least one of them is accelerated. We show that the center-of-mass energy Ecm can become...     

Quasinormal Modes of a Noncommutative-Geometry-Inspired Schwarzschild Black Hole

The quasinormal modes(QNMs) of massless scalar field perturbation in a noncommutative-geometry-inspired Schwarzschild black hole spacetime are studied using the third-order Wentzel-Kramers-Brillouin approximative approach. The result shows that the noncommutative parameter plays an important role for the quasinormal(QNM) frequencies.