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.     

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.     

Creation of Closed or Open Universe from Constrained Instanton

In the no-boundary universe the universe is created from an instanton. However, no instanton exists for the realistic FRW universe with a scalar field. The instanton leading to its quantum creation may be modified and reinterpreted as a constrained gravitational instanton.     

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.     

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.     

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: 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.     

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.     

Time Gauge Fixing and Hilbert Space in Quantum String Cosmology

Recently the low-energy effective string theory has been used by Gasperini and Veneziano to elaborate a very interesting scenario for the early history of the universe (birth of the universe as quantum scattering). Here we investigate the gauge fixing and the problem of the definition of a global time parameter for the quantum form of the model, and obtain the positive norm Hilbert space of states.     

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.     

Letter: Gravitational Entropy of Constrained Instanton

The seeds for quantum creations of universes areconstrained gravitational instantons. For all compactconstrained instantons with a U(1) isometry, the period of the group parameter is identifiedas the reciprocal of the temperature. If remains a free parameter under the constraints, then theEuclidean action becomes the negative of the entropy. Asexamples, we perform the calculations forthe Taub-nut and Taub-Bolt-type models andstudy the quantum creation of the Taub-nutuniverse.     

On a Godel-type Euclidean Solution

We present a two-parameter Godel-type Euclideansolution of the combined gravitational, scalar andelectromagnetic equations of motion. Global propertiesof the solution and particular cases are examined. The possible relevance of this result for theformulation of a quantum field theory in the presence ofclosed timelike curves is considered.     

Non-Singular Charged Black Hole Solution for Non-Linear Source

A non-singular exact black hole solution inGeneral Relativity is presented. The source is anon-linear electrodynamic field, which reduces to theMaxwell theory for weak field. The solution corresponds to a charged black hole with |q| 2s_cm 0.6 m, having metric, curvatureinvariants, and electric field boundedeverywhere.     

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.     

Spherically Symmetric Space-Time with Two Cosmological Constants

We present the analytic spherically symmetric solution of the Einstein equations, which has de Sitter asymptotics for both r and r 0. This two-lambda spherically symmetric solution is globally regular. At the range of mass parameter M_cr1 < M < M_cr2 it has three horizons and describes a neutral black hole whose singularity is replaced by a cosmological constant of Planck or GUT scale, at the background of small . Global structure of space-time contains an infinite sequence of black and white holes, de Sitter-like past and future regular cores (with + at r 0) replacing singularities, asymptotically de Sitter external universes (with for r ), and spacelike infinities. In the range of mass parameter M < M_cr1 we have a one-horizon solution describing recovered selfgravitating particle-like structure at the background of small , and for M > M_cr2 another one-horizon configuration which can be called de Sitter bag. The solutions with M = M_cr1 and M = M_cr2 represent two extreme states of a neutral nonsingular cosmological black hole.     

The Wave Function of the Universe in New Variables

In this paper we evaluate the wave function of the universe using the usual Euclidean path integral technique as proposed by Halliwell and Louko for Ashtekar's new variables. Also we consider the new regularization technique developed by Ishikawa and Ueda for evaluation of the path integral. The wave function by solving the Wheeler-DeWitt equation is also presented.     

Relativistic Hydrodynamic Cosmological Perturbations

Relativistic cosmological perturbation analysescan be made based on several different fundamental gaugeconditions. In the pressureless limit the variables incertain gauge conditions show the correct Newtonian behaviors. Considering the generalcurvature (K) and the cosmological constant ()in the background medium, the perturbed density in thecomoving gauge, and the perturbed velocity and the perturbed potential in the zero-shear gaugeshow the same behavior as the Newtonian ones in generalscales. In the first part, we elaborate these Newtoniancorrespondences. In the second part, using the identified gauge-in variant variables withcorrect Newtonian correspondences, we present therelativistic results with general pressures in thebackground and perturbation. We present the generalsuper-sound-horizon scale solutions of the above mentionedvariables valid for general K, Lambda, and generallyevolving equation of state. We show that, for vanishingK, the super-sound-horizon scale evolution ischaracterised by a conserved variable which is the perturbedthree-space curvature in the comoving gauge. We alsopresent equations for the multi-component hydrodynamicsituation and for the rotation and gravitational wave.