Finite upper bound for the Hawking decay time of an arbitrarily large black hole in anti-de Sitter spacetime

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 rh and mass M∼rhd-3/G has a total decay time to Hawking emission of td∼rhd-1/G∼G2/(d-3)M(d-1)/(d-3) which grows without bound as the radius rh and mass M are taken to infinity. However, in asymptotically anti-de Sitter spacetime with a length scale â"" 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 â""d-1/G.