Static quantum corrections to the Schwarzschild spacetime

TL;DR

This paper investigates quantum corrections to the Schwarzschild black hole metric in the Boulware vacuum, revealing a near-horizon minimum and a potential singularity, using numerical solutions of semiclassical Einstein equations.

Contribution

It provides a numerical analysis of static quantum corrections to Schwarzschild spacetime considering vacuum polarization effects, highlighting a new near-horizon feature and singularity formation.

Findings

Quantum effects cause a minimum in the radial function near the horizon.

The metric component g_{00} becomes very small but non-zero at this minimum.

A curvature singularity emerges beyond the bouncing point.

Abstract

We study static quantum corrections of the Schwarzschild metric in the Boulware vacuum state. Due to the absence of a complete analytic expression for the full semiclassical Einstein equations we approach the problem by considering the s-wave approximation and solve numerically the associated backreaction equations. The solution, including quantum effects due to pure vacuum polarization, is similar to the classical Schwarzschild solution up to the vicinity of the classical horizon. However, the radial function has a minimum at a time-like surface close to the location of the classical event horizon. There the g_{00} component of the metric reaches a very small but non-zero value. The analysis unravels how a curvature singularity emerges beyond this bouncing point. We briefly discuss the physical consequences of these results by extrapolating them to a dynamical collapsing scenario.