On Quantum Deformation of the Schwarzschild Solution

TL;DR

This paper explores how quantum fluctuations deform the Schwarzschild black hole solution, resulting in a regularized space-time with a finite curvature at a minimal radius, replacing the classical singularity.

Contribution

It introduces a quantum deformation of the Schwarzschild solution using effective two-dimensional dilaton gravity, showing the singularity is replaced by a finite-radius regular surface.

Findings

The Schwarzschild singularity shifts to a finite radius near the Planck scale.

The space-time becomes regular with finite scalar curvature at the minimal radius.

The solution describes two asymptotically flat sheets connected at a finite radius.

Abstract

We consider the deformation of the Schwarzschild solution in general relativity due to spherically symmetric quantum fluctuations of the metric and the matter fields. In this case, the 4D theory of gravity with Einstein action reduces to the effective two-dimensional dilaton gravity. We have found that the Schwarzschild singularity at $r=0$ is shifted to the finite radius $r_{min} \sim r_{Pl}$, where the scalar curvature is finite, so that the space-time looks regular and consists of two asymptotically flat sheets glued at the hypersurface of constant radius.