Semiclassical zero-temperature corrections to Schwarzschild spacetime and holography

Motivated by the quest for black holes in anti-de Sitter braneworlds, and, in particular, by the holographic conjecture relating 5D classical bulk solutions with 4D quantum corrected ones, we numerically solve the semiclassical Einstein equations (backreaction equations) with matter fields in the (zero-temperature) Boulware vacuum state. In the absence of an exact analytical expression for < T-mu nu > in four dimensions we work within the s-wave approximation. Our results show that the quantum corrected solution is very similar to Schwarzschild spacetime until very close to the horizon, but then a bouncing surface for the radial function appears which prevents the formation of an event horizon. We also analyze the behavior of the geometry beyond the bounce, where a curvature singularity arises. In the dual theory, this indicates that the corresponding 5D static classical braneworld solution is not a black hole but rather a naked singularity.