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

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 $M\sim r_h^{d-3}/G$ has a total decay time to Hawking emission of $t_d\sim r_h^{d-1}/G\sim G^{2/(d-3)}{M}^{(d-1)/(d-3)}$ 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 $\ell$ 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 ${\ell }^{d-1}/G$.