Particle creation by de Sitter black holes revisited

Abstract

Creation of thermal distribution of particles by a black hole is independent of the detail of gravitational collapse, making the construction of the eternal horizons suffice to address the problem in asymptotically flat spacetimes. For eternal de Sitter black holes however, earlier studies have shown the existence of both thermal and non-thermal particle creation, originating from the non-trivial causal structure of these spacetimes. Keeping this in mind we consider this problem in the context of a quasistationary gravitational collapse occurring in a (3 + 1)-dimensional eternal de Sitter, settling down to a Schwarzschild-or Kerr-de Sitter spacetime and consider a massless minimally coupled scalar field. There is a unique choice of physically meaningful 'in' vacuum here, defined with respect to the positive frequency cosmological Kruskal modes localised on the past cosmological horizon C − , at the onset of the collapse. We define our 'out' vacuum at a fixed radial coordinate 'close' to the future cosmological horizon, C + , with respect to positive frequency outgoing modes written in terms of the ordinary retarded null coordinate, u. We trace such modes back to C − along past directed null geodesics through the collapsing body. Some part of the wave will be reflected back without entering it due to the greybody effect. We show that these two kind of traced back modes yield the two temperature spectra and fluxes subject to the aforementioned 'in' vacuum. Since the coordinate u used in the 'out' modes is not well defined on a horizon, estimate on how 'close' we might be to C + is given by estimating backreaction. We argue no other reasonable choice of the 'out' vacuum would give rise to any thermal spectra. Our conclusions remain valid for all non-Nariai class black holes, irrespective of the relative sizes of the two horizons.

Schottky anomaly of deSitter black holes

“…More recently [24] has computed the black hole and cosmological particle production in SdS spacetimes, choosing a set of particle states such that both spectra are thermal at temperatures respectively of T b and T c . However, in this formulation the particle states are not well behaved on the horizons.…”

Black hole and cosmological particle production in Schwarzschild de Sitter

“…A second relevant example studied recently [12] is the SdS black hole with the choice of modes chosen to closely parallel the Schwarzchild calculation. The past modes on H − b are defined with respect to Kruskal time U b , but unlike our calculation, the future modes are defined with respect to the static patch null coordinate u on a null surface near the cosmological horizon.…”

“…The past modes on H − b are defined with respect to Kruskal time U b , but unlike our calculation, the future modes are defined with respect to the static patch null coordinate u on a null surface near the cosmological horizon. It is found [12] that…”

“…Hence when the static coordinate plane waves are chosen for the future modes, the difference in the amplitudes between SdS and Schwarzchild only appears in the different greybody factors, for the same value of κ b . Reference [12] also derives an analogous expression for the cos-…”

“…Beyond the fact that T b and T c naturally appear in the first laws for SdS (6) and (7) [13], which extends to slow roll inflation [21] [12]. References [20] and [26] attach thermal significance to the radius at which df /dr = 0, the former using holographic arguments.…”