Semiclassical zero-temperature corrections to Schwarzschild spacetime and holography

TL;DR

This paper numerically investigates quantum corrections to Schwarzschild spacetime in the zero-temperature Boulware vacuum, revealing that quantum effects prevent horizon formation and lead to a naked singularity in the dual braneworld scenario.

Contribution

It provides the first numerical analysis of semiclassical backreaction in Schwarzschild spacetime within the s-wave approximation, connecting quantum corrections to holographic duality.

Findings

Quantum corrections cause a bounce preventing horizon formation.

A curvature singularity appears beyond the bounce.

The dual 5D solution is a naked singularity, not a black hole.

Abstract

Motivated by the quest for black holes in AdS 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 till 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.