Black hole evaporation and semiclassicality at large D

TL;DR

This paper investigates the conditions under which large D black holes can be accurately described semiclassically, revealing that rapid evaporation and scrambling impose stricter bounds than small curvature at high dimensions.

Contribution

It identifies that at large D, semiclassicality requires bounds on the rate of change and information scrambling, not just small curvature, due to enhanced Hawking radiation effects.

Findings

Semiclassical description requires entropy S ≥ D^{D+3} log D at large D.

Black holes scramble information faster than they evaporate at large D.

Rapid evaporation constrains the validity of semiclassical models in high dimensions.

Abstract

Black holes of sufficiently large initial radius are expected to be well described by a semiclassical analysis at least until half of their initial mass has evaporated away. For a small number of spacetime dimensions, this holds as long as the black hole is parametrically larger than the Planck length. In that case, curvatures are small and backreaction onto geometry is expected to be well described by a time-dependent classical metric. We point out that at large $D$, small curvature is insufficient to guarantee a valid semiclassical description of black holes. Instead, the strongest bounds come from demanding that the rate of change of the geometry is small and that black holes scramble information faster than they evaporate. This is a consequence of the enormous power of Hawking radiation in $D$-dimensions due to the large available phase space and the resulting minuscule evaporation times. Asymptotically, only black holes with entropies $S \geq D^{D+3} \log D$ are semiclassical. We comment on implications for realistic quantum gravity models in $D \leq 26$ as well as relations to bounds on theories with a large number of gravitationally interacting light species.