Quantization of the interior Schwarzschild black hole

TL;DR

This paper develops a quantum Hamiltonian formalism for the interior of Schwarzschild black holes, deriving a mass spectrum through Wheeler-DeWitt quantization, providing insights into black hole quantum properties.

Contribution

It introduces a Hamiltonian quantum model for Schwarzschild black hole interiors and derives the black hole mass spectrum via Wheeler-DeWitt quantization.

Findings

Mass of the black hole is a Dirac observable.

Quantization yields a discrete mass spectrum.

Classical interior metric is recovered from the model.

Abstract

We study a Hamiltonian quantum formalism of a spherically symmetric space-time which can be identified with the interior of a Schwarzschild black hole. The phase space of this model is spanned by two dynamical variables and their conjugate momenta. It is shown that the classical Lagrangian of the model gives rise the interior metric of a Schwarzschild black hole. We also show that the the mass of such a system is a Dirac observable and then by quantization of the model by Wheeler-DeWitt approach and constructing suitable wave packets we get the mass spectrum of the black hole.