Cutoff Anti–de Sitter Space/Conformal-Field-Theory Duality and the Quest for Braneworld Black Holes

Significant evidence is presented in favor of the holographic conjecture that “4D black holes localized on the brane found by solving the classical bulk equations in ${\mathrm{A}\mathrm{d}\mathrm{S}}_5$ are quantum corrected black holes and not classical ones.” The quantum correction to the Newtonian potential is computed using a numerical computation of $⟨T_{ab}⟩$ in Schwarzschild spacetime for matter fields in the zero-temperature Boulware vacuum state. For the conformally invariant scalar field the leading order term is equivalent to that previously obtained in the weak-field approximation using Feynman diagrams and which has been shown to be equivalent, via the anti–de Sitter space/conformal-field-theory (AdS/CFT) duality, to the analogous calculation in Randall-Sundrum braneworlds. The 4D backreaction equations are used to make a prediction about the existence and the possible spacetime structure of macroscopic static braneworld black holes.

Figure 1

The curves from top to bottom at the right of the plot correspond to $C^t{}_t$, $C^r{}_r$, and $C^{\theta }{}_{\theta }$, respectively.

Figure 2

The curves from top to bottom at the right of the plot correspond to $D^{\theta }{}_{\theta }$, $D^t{}_t$, and $D^r{}_r$ respectively.