Black hole evaporation in an expanding universe

Abstract

We calculate the quantum radiation power of black holes which are asymptotic to the Einsteinde 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⊙) 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.

Black holes in the Universe: Generalized Lemaître-Tolman-Bondi solutions

“…The purpose of the present paper is to derive such new solutions representing a black hole in a FRW universe with a cosmic fluid consisting of dark matter, or of dark matter plus dark energy (possibly a cosmological constant), or of quintom matter [32]. These types of solution are also useful, if nothing else as toy models, in the study of dynamical horizons and their thermodynamics [22,[42][43][44][45] and of primordial black holes [33] as probes of the early universe [34,35].…”

Hawking temperature for near-equilibrium black holes

“…It would be interesting to study the properties of κ(u) for black holes in an expanding universe, such as those discussed in Refs. [5,28], for which the derivation is similar to the case of asymptotically flat spacetime. In the case of asymptotically AdS spacetime, in the Poincaré chart the past horizon, which is the Cauchy horizon, exists even in the pure AdS spacetime.…”

“…If black hole thermodynamics is robust enough, such insight on usual thermodynamic systems leads to the above expectation on dynamical spacetimes and black holes. Many studies have been made on generalizing Hawking temperature for dynamical black hole approaches [4][5][6][7][8][9][10], and they support such an expectation.…”

Conformal transformation, near horizon symmetry, Virasoro algebra, and entropy

“…To obtain a full thermodynamics of such spacetimes, one needs to correctly obtain each entities from the first principle. For instance, in [26,21] the temperature was determined by calculating the radiation spectrum from the horizon. But in literature no derivation of entropy exists.…”