Quantum Hamiltonian for gravitational collapse

TL;DR

This paper develops a Hamiltonian framework for quantum gravitational collapse using spherically symmetric gravity-scalar field theory, enabling numerical studies and addressing conceptual issues in quantum dynamics.

Contribution

It introduces a reduced Hamiltonian operator tailored for quantum gravitational collapse in a spherically symmetric setting, integrating null expansion operators.

Findings

Framework for numerical implementation of quantum gravitational collapse.

Discussion of conceptual issues in quantum dynamics with partial gauge fixing.

Construction of a reduced Hamiltonian operator for the gravity-scalar field system.

Abstract

Using a Hamiltonian formulation of the spherically symmetric gravity-scalar field theory adapted to flat spatial slicing, we give a construction of the reduced Hamiltonian operator. This Hamiltonian, together with the null expansion operators presented in an earlier work, form a framework for studying gravitational collapse in quantum gravity. We describe a setting for its numerical implementation, and discuss some conceptual issues associated with quantum dynamics in a partial gauge fixing.