Flat slice Hamiltonian formalism for dynamical black holes

TL;DR

This paper develops a Hamiltonian formalism for spherically symmetric, asymptotically flat black hole models using flat slice coordinates, simplifying the Hamiltonian structure for potential quantization.

Contribution

It introduces a new Hamiltonian analysis in flat slice coordinates, leading to a simpler form suitable for quantization of black hole models.

Findings

Derived a Hamiltonian action principle with an asymptotic mass formula

Performed a time gauge fixing resulting in a local density Hamiltonian

Simplified Hamiltonian form compared to Schwarzschild gauge

Abstract

We give a Hamiltonian analysis of the asymptotically flat spherically symmetric system of gravity coupled to a scalar field. This 1+1 dimensional field theory may be viewed as the "standard model" for studying black hole physics. Our analysis is adapted to the flat slice Painleve-Gullstrand coordinates. We give a Hamiltonian action principle for this system, which yields an asymptotic mass formula. We then perform a time gauge fixing that gives a Hamiltonian as the integral of a local density. The Hamiltonian takes a relatively simple form compared to earlier work in Schwarzschild gauge, and therefore provides a setting amenable to full quantisation.