Cutoff AdS/CFT duality and the quest for braneworld black holes

TL;DR

This paper provides evidence supporting the idea that 4D black holes on branes are quantum-corrected, not classical, by calculating quantum corrections to the Newtonian potential using holographic duality and numerical methods.

Contribution

It demonstrates the quantum nature of brane black holes through numerical computation of stress-energy tensor and links it to holographic duality and previous weak-field results.

Findings

Quantum correction to Newtonian potential: M/45πr^3

Numerical verification of stress-energy tensor in Schwarzschild spacetime

Support for quantum-corrected black holes in braneworld scenarios

Abstract

We present significant evidence in favour of the holographic conjecture that ``4D black holes localized on the brane found by solving the classical bulk equations in $AdS_5$ are quantum corrected black holes and not classical ones''. The crucial test is the calculation of the quantum correction to the Newtonian potential based on a numerical computation of $<T^a_b>$ in Schwarzschild spacetime for matter fields in the zero temperature Boulware vacuum state. For the case of the conformally invariant scalar field the leading order term is found to be $M/45\pi r^3$. This result is equivalent to the result which was previously obtained in the weak-field approximation using Feynman diagrams and which has been shown to be equivalent, via the AdS/CFT duality, to the analogous calculation in Randall-Sundrum braneworlds. This asymptotic behavior was not captured in the analytical approximations for $<T^a_b>$ proposed in the literature. The 4D backreaction equations are then used to make a prediction about the existence and the possible spacetime structure of macroscopic static braneworld black holes.