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

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 $M/45πr^3$. 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.

4 pages, 2 figures