A generalization of the Hawking black hole area theorem

TL;DR

This paper extends the classical black hole area theorem by proving it under weaker, averaged energy conditions and introduces bounds on black hole horizon shrinking, relevant for quantum effects.

Contribution

It generalizes the classical theorem to include averaged energy conditions and provides bounds applicable even when classical energy conditions are violated.

Findings

Proves the area theorem with an averaged energy condition.

Establishes bounds on black hole horizon shrinking.

Applies bounds to cases violating classical energy conditions.

Abstract

Hawking's black hole area theorem was proven using the null energy condition (NEC), a pointwise condition violated by quantum fields. The violation of the NEC is usually cited as the reason that black hole evaporation is allowed in the context of semiclassical gravity. Here we provide two generalizations of the classical black hole area theorem: First, a proof of the original theorem with an averaged condition, the weakest possible energy condition to prove the theorem using focusing of null geodesics. Second, a proof of an area-type result that allows for the shrinking of the black hole horizon but provides a bound on it. This bound can be translated to a bound on the black hole evaporation rate using a condition inspired from quantum energy inequalities. Finally, we show how our bound can be applied to two cases that violate classical energy conditions.