Black hole inner horizon evaporation in semiclassical gravity

Abstract

In this work we analyse the backreaction of a quantum field on a spherically symmetric black hole geometry with an inner horizon, i.e. an internal boundary of the trapped region. We start with a black hole background with an inner horizon which remains static after its formation. We quantise a massless scalar field on it and calculate its renormalised stress–energy tensor in the Polyakov approximation. We use this tensor as a source of perturbation on top of the background spacetime. We find that the inner horizon has a tendency to evaporate outward much more quickly than the outer one evaporates inward through the Hawking effect. This suggests a revised picture of a semiclassically self-consistent evaporation in which the dominant dynamical effect comes from the inner horizon, the cause of which can be seen as an interplay between the well-known unstable nature of this horizon and a locally negative energy contribution from the quantum vacuum. We also look at backreaction on backgrounds which resemble gravitational collapse, where the inner horizon moves towards the origin. There we find that, depending on the nature of the background dynamics, horizon-related semiclassical effects can become dominant and invert the collapse.