One-loop corrections for Schwarzschild black hole via 2D dilaton gravity

TL;DR

This paper investigates quantum one-loop corrections to Schwarzschild black holes using a 2D dilaton gravity framework derived from 4D gravity, analyzing vacuum solutions and thermodynamic modifications.

Contribution

It provides the first perturbative solutions for quantum-corrected Schwarzschild black holes within a 2D dilaton gravity approach, highlighting limitations of the standard effective action.

Findings

Quantum corrections modify black hole thermodynamics.

Standard effective action cannot reproduce 4D Hartle-Hawking vacuum boundary conditions.

Vacuum solutions are obtained for null-dust and minimally coupled scalar fields.

Abstract

We study quantum corrections for the Schwarzshild black hole by considering it as a vacuum solution of a 2D dilaton gravity theory obtained by spherical reduction of 4D gravity coupled with matter. We find perturbatively the vacuum solution for the standard one-loop effective action in the case of null-dust matter and in the case of minimally coupled scalar field. The corresponding state is in both cases 2D Hartle-Hawking vacuum, and we evaluate the corresponding quantum corrections for the thermodynamical parameters of the black hole. We also find that the standard effective action does not allow boundary conditions corresponding to a 4D Hartle-Hawking vacuum state.