Singularity Resolution of Quantum Black Holes in (A)dS

TL;DR

This paper presents a quantum gravity approach that resolves black hole singularities in (A)dS spacetimes by using unimodular gravity and canonical quantization, leading to a quantum-corrected metric with a transition to white holes.

Contribution

It introduces a novel quantum resolution of black hole singularities using unimodular gravity and derives an analytical quantum-corrected Schwarzschild metric.

Findings

Singularity is resolved in quantum theory with unimodular gravity.

Quantum-corrected metric includes a new length scale $r_{min}$.

Black hole to white hole transition is described analytically.

Abstract

The singularities present at the centre of black holes signal a break down of the classical theory. In this paper, we demonstrate a resolution of the Schwarzschild-(Anti-)de Sitter singularity by imposing unitary evolution with respect to unimodular time. Employing the Henneaux-Teitelboim formulation of unimodular gravity, we perform a canonical quantization on a symmetry-reduced Schwarzschild-(Anti-) de Sitter model. This leads to a Wheeler-DeWitt equation that effectively becomes a Schr\"odinger equation in unimodular time. By imposing unitarity, we discover a family of quantum theories in which the classical singularity is resolved. These theories each allow only semiclassical states corresponding to one mass sign: either positive, negative, or zero. Furthermore, we derive an analytical expression for the quantum-corrected Schwarzschild metric, which is modified by a new length scale $r_{min}$ that governs the black hole's transition to a white hole.