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 Schrödinger 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. The resulting quantum-corrected Schwarzschild metric is modified by a new length scale.