Quantum gravity corrections to the Schwarzschild mass

TL;DR

This paper investigates quantum corrections to the ADM mass of black holes within higher-dimensional vacuum spherically symmetric Einstein gravity, using a conformal sigma model approach and perturbative quantization.

Contribution

It introduces a novel conformal sigma model formulation for higher-dimensional Einstein gravity and estimates quantum corrections to black hole mass.

Findings

Quantum corrections to ADM mass are derived perturbatively.

The conformal sigma model links mass and sphere radius in higher dimensions.

Results provide insights into quantum effects in black hole physics.

Abstract

Vacuum spherically symmetric Einstein gravity in $N\ge 4$ dimensions can be cast in a two-dimensional conformal nonlinear sigma model form by first integrating on the $(N-2)$-dimensional (hyper)sphere and then performing a canonical transformation. The conformal sigma model is described by two fields which are related to the Arnowitt-Deser-Misner mass and to the radius of the $(N-2)$-dimensional (hyper)sphere, respectively. By quantizing perturbatively the theory we estimate the quantum corrections to the ADM mass of a black hole.