Statistical Mechanics of Black Holes

We analyze the statistical mechanics of a gas of neutral and charged black holes. The microcanonical ensemble is the only possible approach to this system, and the equilibrium configuration is the one for which most of the energy is carried by a single black hole. Schwarzschild black holes are found to obey the statistical bootstrap condition. In all cases, the microcanonical temperature is identical to the Hawking temperature of the most massive black hole in the gas. U(1) charges in general break the bootstrap property. The problems of black hole decay and of quantum coherence are also addressed.Comment: 21 page

Discrete Group Actions on Spacetimes: Causality Conditions and the Causal Boundary

Suppose a spacetime $M$ is a quotient of a spacetime $V$ by a discrete group of isometries. It is shown how causality conditions in the two spacetimes are related, and how can one learn about the future causal boundary on $M$ by studying structures in $V$. The relations between the two are particularly simple (the boundary of the quotient is the quotient of the boundary) if both $V$ and $M$ have spacelike future boundaries and if it is known that the quotient of the future completion of $V$ is past-distinguishing. (That last assumption is automatic in the case of $M$ being multi-warped.)Comment: 32 page

Computing the spectrum of black hole radiation in the presence of high frequency dispersion: an analytical approach

We present a method for computing the spectrum of black hole radiation of a scalar field satisfying a wave equation with high frequency dispersion. The method involves a combination of Laplace transform and WKB techniques for finding approximate solutions to ordinary differential equations. The modified wave equation is obtained by adding a higher order derivative term suppressed by powers of a fundamental momentum scale $k_0$ to the ordinary wave equation. Depending on the sign of this new term, high frequency modes propagate either superluminally or subluminally. We show that the resulting spectrum of created particles is thermal at the Hawking temperature, and further that the out-state is a thermal state at the Hawking temperature, to leading order in $k_0$, for either modification.Comment: 26 pages, plain latex, 6 figures included using psfi

Dynamics of Extremal Black Holes

Particle scattering and radiation by a magnetically charged, dilatonic black hole is investigated near the extremal limit at which the mass is a constant times the charge. Near this limit a neighborhood of the horizon of the black hole is closely approximated by a trivial product of a two-dimensional black hole with a sphere. This is shown to imply that the scattering of long-wavelength particles can be described by a (previously analyzed) two-dimensional effective field theory, and is related to the formation/evaporation of two-dimensional black holes. The scattering proceeds via particle capture followed by Hawking re-emission, and naively appears to violate unitarity. However this conclusion can be altered when the effects of backreaction are included. Particle-hole scattering is discussed in the light of a recent analysis of the two-dimensional backreaction problem. It is argued that the quantum mechanical possibility of scattering off of extremal black holes implies the potential existence of additional quantum numbers - referred to as ``quantum whiskers'' - characterizing the black hole.Comment: 31 page

Evanescent Black Holes

A renormalizable theory of quantum gravity coupled to a dilaton and conformal matter in two space-time dimensions is analyzed. The theory is shown to be exactly solvable classically. Included among the exact classical solutions are configurations describing the formation of a black hole by collapsing matter. The problem of Hawking radiation and backreaction of the metric is analyzed to leading order in a $1/N$ expansion, where $N$ is the number of matter fields. The results suggest that the collapsing matter radiates away all of its energy before an event horizon has a chance to form, and black holes thereby disappear from the quantum mechanical spectrum. It is argued that the matter asymptotically approaches a zero-energy ``bound state'' which can carry global quantum numbers and that a unitary $S$-matrix including such states should exist.Comment: 14 page

Trapped surfaces in spherical expanding open universes

Consider spherically symmetric initial data for a cosmology which, in the large, approximates an open $k = -1 ,\Lambda = 0$ Friedmann-Lema{\^\i}tre universe. Further assume that the data is chosen so that the trace of the extrinsic curvature is a constant and that the matter field is at rest at this instant of time. One expects that no trapped surfaces appear in the data if no significant clump of excess matter is to be found. This letter confirms this belief by displaying a necessary condition for the existence of trapped surfaces.This necessary condition, simply stated, says that a relatively large amount of excess matter must be concentrated in a small volume for trapped surfaces to appear.Comment: 8 pages, Late

Smooth transitions from Schwarzschild vacuum to de Sitter space

We provide an infinity of spacetimes which contain part of both the Schwarzschild vacuum and de Sitter space. The transition, which occurs below the Schwarzschild event horizon, involves only boundary surfaces (no surface layers). An explicit example is given in which the weak and strong energy conditions are satisfied everywhere (except in the de Sitter section) and the dominant energy condition is violated only in the vicinity of the boundary to the Schwarzschild section. The singularity is avoided by way of a change in topology in accord with a theorem due to Borde..Comment: revtex4, two figures. Final form to appear in Phys. Rev.

Quantum Black Holes

Static solutions of large-$N$ quantum dilaton gravity in $1+1$ dimensions are analyzed and found to exhibit some unusual behavior. As expected from previous work, infinite-mass solutions are found describing a black hole in equilibrium with a bath of Hawking radiation. Surprisingly, the finite mass solutions are found to approach zero coupling both at the horizon and spatial infinity, with a ``bounce'' off of strong coupling in between. Several new zero mass solutions -- candidate quantum vacua -- are also described.Comment: 14 pages + 6 figure

Black Holes and Massive Remnants

This paper revisits the conundrum faced when one attempts to understand the dynamics of black hole formation and evaporation without abandoning unitary evolution. Previous efforts to resolve this puzzle assume that information escapes in corrections to the Hawking process, that an arbitrarily large amount of information is transmitted by a planckian energy or contained in a Planck-sized remnant, or that the information is lost to another universe. Each of these possibilities has serious difficulties. This paper considers another alternative: remnants that carry large amounts of information and whose size and mass depend on their information content. The existence of such objects is suggested by attempts to incorporate a Planck scale cutoff into physics. They would greatly alter the late stages of the evaporation process. The main drawback of this scenario is apparent acausal behavior behind the horizon.Comment: 16 pages + 3 Fig

Fluctuations in the Cosmic Microwave Background I: Form Factors and their Calculation in Synchronous Gauge

It is shown that the fluctuation in the temperature of the cosmic microwave background in any direction may be evaluated as an integral involving scalar and dipole form factors, which incorporate all relevant information about acoustic oscillations before the time of last scattering. A companion paper gives asymptotic expressions for the multipole coefficient $C_\ell$ in terms of these form factors. Explicit expressions are given here for the form factors in a simplified hydrodynamic model for the evolution of perturbations.Comment: 35 pages, no figures. Improved treatment of damping, including both Landau and Silk damping; inclusion of late-time effects; several references added; minor changes and corrections made. Accepted for publication in Phys. Rev. D1