A local Hamiltonian for spherically symmetric gravity coupled to a scalar field

TL;DR

This paper introduces a gauge fixing for spherically symmetric gravity coupled to a scalar field, resulting in a local Hamiltonian density, which could facilitate quantization including black hole evaporation scenarios.

Contribution

It provides a novel gauge fixing that yields a local Hamiltonian for spherically symmetric gravity with scalar fields, a longstanding challenge.

Findings

Hamiltonian expressed as an integral over a local density

Applicable to a large set of initial data, including black hole evaporation cases

Potentially enables new approaches to quantum gravity in spherical symmetry

Abstract

We present a gauge fixing of gravity coupled to a scalar field in spherical symmetry such that the Hamiltonian is an integral over space of a local density. Such a formulation had proved elusive over the years. As in any gauge fixing, it works for a restricted set of initial data. We argue that the set could be large enough to attempt a quantization the could include the important case of an evaporating black hole.