Spherically symmetric gravity coupled to a scalar field with a local Hamiltonian: the complete initial-boundary value problem using metric variables

TL;DR

This paper presents a gauge fixing of spherically symmetric gravity coupled to a scalar field, resulting in a local Hamiltonian in metric variables, and fully specifies the initial-boundary value problem for ingoing Gaussian pulses.

Contribution

It introduces a gauge fixing in metric variables that yields a local Hamiltonian for spherical gravity with a scalar field, extending previous work with Ashtekar variables.

Findings

Complete initial-boundary value problem specified for ingoing Gaussian pulses.

Hamiltonian expressed as a local density in metric variables.

Framework applicable to numerical simulations of scalar field collapse.

Abstract

We discuss 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. In a previous paper we had presented it using Ashtekar's new variables. Here we study it in metric variables. We specify completely the initial-boundary value problem for ingoing Gaussian pulses.