Quantum Schwarzschild-(A)dS Black Holes: Unitarity and Singularity Resolution

TL;DR

This paper presents a quantum model of Schwarzschild-(A)dS black holes within unimodular gravity, demonstrating how quantum effects can resolve singularities and allow for a consistent, unitary evolution between black and white hole states.

Contribution

It introduces a novel quantisation approach in unimodular gravity, deriving quantum-corrected, nonsingular black hole solutions with a well-defined unitarity framework and a family of physically motivated boundary conditions.

Findings

Quantum-corrected black hole metrics are nonsingular.

Unitarity is maintained through self-adjoint extensions of the Hamiltonian.

The model allows for a quantum transition between black and white hole states.

Abstract

We consider the canonical quantisation of spherically symmetric spacetimes within unimodular gravity, leaving sign choices in the metric general enough to include both the interior and exterior Schwarzschild-(Anti-)de Sitter spacetime. In unimodular gravity the cosmological constant appears as an integration constant analogous to a total energy, and the quantum Wheeler-DeWitt equation takes the form of a Schr\"odinger equation in unimodular time. We discuss self-adjoint extensions of the Schr\"odinger-like Hamiltonian arising from the requirement of unitarity in unimodular time, and identify a physically motivated one-parameter family of extensions. For semiclassical states we are able to derive analytical expressions for expectation values of the metric, representing a quantum-corrected, nonsingular extension of the classical Schwarzschild-(A)dS geometry which describes a quantum transition between asymptotic black hole and white hole states. The sign of the self-adjoint extension parameter corresponds to the allowed sign of the black hole/white hole mass, and so it can be chosen to ensure that this mass is always positive. We also discuss tunnelling states which allow for a change in the sign of the mass, but which are not semiclassical in high-curvature regions. Our mechanism for singularity resolution and the explicit form of the quantum-corrected metric can be compared to other proposals for black holes in quantum gravity, and in the asymptotically AdS case can be contrasted with holographic arguments.