Finite Upper Bound for the Hawking Decay Time of an Arbitrarily Large Black Hole in Anti-de Sitter Spacetime

TL;DR

This paper demonstrates that in anti-de Sitter spacetime, the Hawking decay time of large black holes remains finite and bounded by a scale related to the spacetime's length, contrasting with the unbounded decay time in flat spacetime.

Contribution

It establishes a finite upper bound for the Hawking decay time of arbitrarily large black holes in anti-de Sitter spacetime, unlike in flat spacetime where decay time diverges.

Findings

Decay time remains bounded by l^{d-1}/G in AdS spacetime.

Decay time diverges with size in flat spacetime.

Boundary conditions influence black hole evaporation times.

Abstract

In an asymptotically flat spacetime of dimension d > 3 and with the Newtonian gravitational constant G, a spherical black hole of initial horizon radius r_h and mass M ~ r_h^{d-3}/G has a total decay time to Hawking emission of t_d ~ r_h^{d-1}/G ~ G^{2/(d-3)}M^{(d-1)/(d-3)} which grows without bound as the radius r_h and mass M are taken to infinity. However, in asymptotically anti-de Sitter spacetime with a length scale l and with absorbing boundary conditions at infinity, the total Hawking decay time does not diverge as the mass and radius go to infinity but instead remains bounded by a time of the order of l^{d-1}/G.