Black Hole Evaporation in an Expanding Universe

We calculate the quantum radiation power of black holes which are asymptotic to the Einstein-de Sitter universe at spatial and null infinities. We consider two limiting mass accretion scenarios, no accretion and significant accretion. We find that the radiation power strongly depends on not only the asymptotic condition but also the mass accretion scenario. For the no accretion case, we consider the Einstein-Straus solution, where a black hole of constant mass resides in the dust Friedmann universe. We find negative cosmological correction besides the expected redshift factor. This is given in terms of the cubic root of ratio in size of the black hole to the cosmological horizon, so that it is currently of order $10^{-5} (M/10^{6}M_{\odot})^{1/3} (t/14 {Gyr})^{-1/3}$ but could have been significant at the formation epoch of primordial black holes. Due to the cosmological effects, this black hole has not settled down to an equilibrium state. This cosmological correction may be interpreted in an analogy with the radiation from a moving mirror in a flat spacetime. For the significant accretion case, we consider the Sultana-Dyer solution, where a black hole tends to increase its mass in proportion to the cosmological scale factor. In this model, we find that the radiation power is apparently the same as the Hawking radiation from the Schwarzschild black hole of which mass is that of the growing mass at each moment. Hence, the energy loss rate decreases and tends to vanish as time proceeds. Consequently, the energy loss due to evaporation is insignificant compared to huge mass accretion onto the black hole. Based on this model, we propose a definition of quasi-equilibrium temperature for general conformal stationary black holes.Comment: Accepted for publication in Class.Quant.Grav., 18 pages and 3 figure

Gravitational energy

Observers at rest in a stationary spacetime flat at infinity can measure small amounts of rest-mass+internal energies+kinetic energies+pressure energy in a small volume of fluid attached to a local inertial frame. The sum of these small amounts is the total "matter energy" for those observers. The total mass-energy minus the matter energy is the binding gravitational energy. Misner, Thorne and Wheeler evaluated the gravitational energy of a spherically symmetric static spacetime. Here we show how to calculate gravitational energy in any static and stationary spacetime for isolated sources with a set of observers at rest. The result of MTW is recovered and we find that electromagnetic and gravitational 3-covariant energy densities in conformastatic spacetimes are of opposite signs. Various examples suggest that gravitational energy is negative in spacetimes with special symmetries or when the energy-momentum tensor satisfies usual energy conditions.Comment: 12 pages. Accepted for publication in Class. Quantum Gra

Gyratons on Melvin spacetime

We present and analyze new exact gyraton solutions of algebraic type II on a background which is static, cylindrically symmetric Melvin universe of type D. For a vanishing electromagnetic field it reduces to previously studied gyratons on Minkowski background. We demonstrate that the solutions are member of a more general family of the Kundt spacetimes. We show that the Einstein equations reduce to a set of mostly linear equations on a transverse 2-space and we discuss the properties of polynomial scalar curvature invariants which are generally non-constant but unaffected by the presence of gyratons.Comment: 15 pages, no figures, journal version extended by appendices B and

Spherically symmetric space-time with the regular de Sitter center

The requirements are formulated which lead to the existence of the class of globally regular solutions to the minimally coupled GR equations which are asymptotically de Sitter at the center. The brief review of the resulting geometry is presented. The source term, invariant under radial boots, is classified as spherically symmetric vacuum with variable density and pressure, associated with an r-dependent cosmological term, whose asymptotic in the origin, dictated by the weak energy condition, is the Einstein cosmological term. For this class of metrics the ADM mass is related to both de Sitter vacuum trapped in the origin and to breaking of space-time symmetry. In the case of the flat asymptotic, space-time symmetry changes smoothly from the de Sitter group at the center to the Lorentz group at infinity. Dependently on mass, de Sitter-Schwarzschild geometry describes a vacuum nonsingular black hole, or G-lump - a vacuum selfgravitating particlelike structure without horizons. In the case of de Sitter asymptotic at infinity, geometry is asymptotically de Sitter at both origin and infinity and describes, dependently on parameters and choice of coordinates, a vacuum nonsingular cosmological black hole, selfgravitating particlelike structure at the de Sitter background and regular cosmological models with smoothly evolving vacuum energy density.Comment: Latex, 10 figures, extended version of the plenary talk at V Friedmann Intern. Conf. on Gravitation and Cosmology, Brazil 2002, to appear in Int.J.Mod.Phys.

Microscopic expressions for the thermodynamic temperature

We show that arbitrary phase space vector fields can be used to generate phase functions whose ensemble averages give the thermodynamic temperature. We describe conditions for the validity of these functions in periodic boundary systems and the Molecular Dynamics (MD) ensemble, and test them with a short-ranged potential MD simulation.Comment: 21 pages, 2 figures, Revtex. Submitted to Phys. Rev.

Black hole evaporation in a heat bath as a nonequilibrium process and its final fate

When a black hole evaporates, there arises a net energy flow from black hole into its outside environment (heat bath). The existence of energy flow means that the thermodynamic state of the whole system, which consists of the black hole and the heat bath, is in a nonequilibrium state. Therefore, in order to study the detail of evaporation process, the nonequilibrium effects of the energy flow should be taken into account. Using the nonequilibrium thermodynamics which has been formulated recently, this paper shows the following: (1) Time scale of black hole evaporation in a heat bath becomes shorter than that of the evaporation in an empty space (a situation without heat bath), because a nonequilibrium effect of temperature difference between the black hole and heat bath appears as a strong energy extraction from the black hole by the heat bath. (2) Consequently a huge energy burst (stronger than that of the evaporation in an empty space) arises at the end of semi-classical stage of evaporation. (3) It is suggested that a remnant of Planck size remains after the quantum stage of evaporation in order to guarantee the increase of total entropy of the whole system

The mass formula for quasi-black holes

A quasi-black hole, either non-extremal or extremal, can be broadly defined as the limiting configuration of a body when its boundary approaches the body's quasihorizon. We consider the mass contributions and the mass formula for a static quasi-black hole. The analysis involves careful scrutiny of the surface stresses when the limiting configuration is reached. It is shown that there exists a strict correspondence between the mass formulas for quasi-black holes and pure black holes. This perfect parallelism exists in spite of the difference in derivation and meaning of the formulas in both cases. For extremal quasi-black holes the finite surface stresses give zero contribution to the total mass. This leads to a very special version of Abraham-Lorentz electron in general relativity in which the total mass has pure electromagnetic origin in spite of the presence of bare stresses.Comment: 22 page

Topological Defects in Contracting Universes

We study the behaviour and consequences of cosmic string networks in contracting universes. They approximately behave during the collapse phase as a radiation fluids. Scaling solutions describing this are derived and tested against high-resolution numerical simulations. A string network in a contracting universe, together with the gravitational radiation it generates, can affect the dynamics of the universe both locally and globally, and be an important source of radiation, entropy and inhomogeneity. We discuss possible implications for bouncing and cyclic models.Comment: Shorter version of astro-ph/0206287. To appear in Phys. Rev. Let

Low-energy sector quantization of a massless scalar field outside a Reissner-Nordstrom black hole and static sources

We quantize the low-energy sector of a massless scalar field in the Reissner-Nordstrom spacetime. This allows the analysis of processes involving soft scalar particles occurring outside charged black holes. In particular, we compute the response of a static scalar source interacting with Hawking radiation using the Unruh (and the Hartle-Hawking) vacuum. This response is compared with the one obtained when the source is uniformly accelerated in the usual vacuum of the Minkowski spacetime with the same proper acceleration. We show that both responses are in general different in opposition to the result obtained when the Reissner-Nordstrom black hole is replaced by a Schwarzschild one. The conceptual relevance of this result is commented.Comment: 12 pages (REVTEX), no figure

Evolution of the density contrast in inhomogeneous dust models

With the help of families of density contrast indicators, we study the tendency of gravitational systems to become increasingly lumpy with time. Depending upon their domain of definition, these indicators could be local or global. We make a comparative study of these indicators in the context of inhomogeneous cosmological models of Lemaitre--Tolman and Szekeres. In particular, we look at the temporal asymptotic behaviour of these indicators and ask under what conditions, and for which class of models, they evolve monotonically in time. We find that for the case of ever-expanding models, there is a larger class of indicators that grow monotonically with time, whereas the corresponding class for the recollapsing models is more restricted. Nevertheless, in the absence of decaying modes, indicators exist which grow monotonically with time for both ever-expanding and recollapsing models simultaneously. On the other hand, no such indicators may found which grow monotonically if the decaying modes are allowed to exist. We also find the conditions for these indicators to be non-divergent at the initial singularity in both models. Our results can be of potential relevance for understanding structure formation in inhomogeneous settings and in debates regarding gravitational entropy and arrow of time. In particular, the spatial dependence of turning points in inhomogeneous cosmologies may result in multiple density contrast arrows in recollapsing models over certain epochs. We also find that different notions of asymptotic homogenisation may be deduced, depending upon the density contrast indicators used.Comment: 22 pages, 1 figure. To be published in Classical and Quantum Gravit