Holography and trace anomaly: what is the fate of (brane-world) black holes?

TL;DR

This paper explores the relationship between holography, trace anomaly, and black hole stability in brane-world scenarios, suggesting that static black holes may be unstable and proposing a time-dependent model for evaporating black holes.

Contribution

It introduces a novel use of the trace anomaly to assess the stability of brane-world black holes within the holographic framework.

Findings

Trace anomaly indicates potential instability of static brane black holes.

Time-dependent metrics better represent late-stage black hole evaporation.

Holographic relations connect bulk gravitational perturbations to boundary quantum effects.

Abstract

The holographic principle relates (classical) gravitational waves in the bulk to quantum fluctuations and the Weyl anomaly of a conformal field theory on the boundary (the brane). One can thus argue that linear perturbations in the bulk of static black holes located on the brane be related to the Hawking flux and that (brane-world) black holes are therefore unstable. We try to gain some information on such instability from established knowledge of the Hawking radiation on the brane. In this context, the well-known trace anomaly is used as a measure of both the validity of the holographic picture and of the instability for several proposed static brane metrics. In light of the above analysis, we finally consider a time-dependent metric as the (approximate) representation of the late stage of evaporating black holes which is characterized by decreasing Hawking temperature, in qualitative agreement with what is required by energy conservation.