On Quantum Deformation of the Schwarzschild Solution

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.