Quantum Black Holes as Holograms in AdS Braneworlds

TL;DR

The paper proposes that black holes localized on a brane in AdS braneworlds represent quantum-corrected $D$-dimensional black holes of a cutoff CFT coupled to gravity, so classical bulk dynamics encode planar quantum corrections via the holographic dual. It tests this through detailed analyses in $D=3$ (AdS$_4$/AdS$_3$) where quantum Casimir backreaction dresses conical singularities into horizons and yields quantum-corrected BTZ black holes, and discusses $D=4$ where Hawking radiation maps to bulk gravitational bremsstrahlung in AdS$_5$; static brane black holes are argued not to exist due to Hawking backreaction, with radiating exteriors described by Vaidya-type geometries and anomaly constraints guiding the matching. The work provides a unifying holographic framework for quantum black hole effects on branes, explains quantum censorship in 2+1 dimensions, and offers a physically transparent bulk picture for Hawking radiation in braneworld gravity, while outlining important open questions about vacuum choice and bulk dynamics. Overall, the study strengthens the interpretive power of AdS/CFT in braneworld contexts and motivates further exploration of time-dependent bulk solutions and their CFT duals.

Abstract

We propose a new approach for using the AdS/CFT correspondence to study quantum black hole physics. The black holes on a brane in an AdS$_{D+1}$ braneworld that solve the classical bulk equations are interpreted as duals of {\it quantum-corrected} $D$-dimensional black holes, rather than classical ones, of a conformal field theory coupled to gravity. We check this explicitly in D=3 and D=4. In D=3 we reinterpret the existing exact solutions on a flat membrane as states of the dual 2+1 CFT. We show that states with a sufficiently large mass really are 2+1 black holes where the quantum corrections dress the classical conical singularity with a horizon and censor it from the outside. On a negatively curved membrane, we reinterpret the classical bulk solutions as quantum-corrected BTZ black holes. In D=4 we argue that the bulk solution for the brane black hole should include a radiation component in order to describe a quantum-corrected black hole in the 3+1 dual. Hawking radiation of the conformal field is then dual to classical gravitational bremsstrahlung in the AdS$_5$ bulk.