Gravitational collapse and black hole evolution: do holographic black holes eventually "anti-evaporate"?

TL;DR

This paper investigates the gravitational collapse of stars in Brane-World models, revealing conditions under which black holes can undergo a process of evaporation followed by anti-evaporation, influenced by holographic effects and back-reaction.

Contribution

It introduces a novel analysis of black hole evolution in Brane-World scenarios, highlighting the roles of holographic effects and back-reaction in black hole evaporation and anti-evaporation.

Findings

Stars can evaporate and then re-expand in Brane-World models.

Holographic effects influence black hole dynamics and energy exchange.

A new bound for brane tension is derived.

Abstract

We study the gravitational collapse of compact objects in the Brane-World. We begin by arguing that the regularity of the five-dimensional geodesics does not allow the energy-momentum tensor of matter on the brane to have (step-like) discontinuities, which are instead admitted in the four-dimensional General Relativistic case, and compact sources must therefore have an atmosphere. Under the simplifying assumption that matter is a spherically symmetric cloud of dust without dissipation, we can find the conditions for which the collapsing star generically ``evaporates'' and approaches the Hawking behavior as the (apparent) horizon is being formed. Subsequently, the apparent horizon evolves into the atmosphere and the back-reaction on the brane metric reduces the evaporation, which continues until the effective energy of the star vanishes. This occurs at a finite radius, and the star afterwards re-expands and ``anti-evaporates''. We clarify that the Israel junction conditions across the brane (holographically related to the matter trace anomaly) and the projection of the Weyl tensor on the brane (holographically interpreted as the quantum back-reaction on the brane metric) contribute to the total energy as, respectively, an ``anti-evaporation'' and an ``evaporation'' term. Concluding, we comment on the possible effects of dissipation and obtain a new stringent bound for the brane tension.