A Partially Gauged Fixed Hamiltonian for Scalar Field Collapse

TL;DR

This paper derives a simplified, partially gauge-fixed Hamiltonian for scalar field collapse leading to black hole formation, applicable across various theories and dimensions, facilitating quantum studies of black hole dynamics.

Contribution

It introduces a new, simple Hamiltonian framework for scalar field collapse that is compatible with regular horizon coordinates and applicable to multiple models.

Findings

Hamiltonian is remarkably simple and consistent with Painleve-Gullstrand coordinates.

Framework applies to spherically symmetric black holes in various dimensions.

Provides a foundation for quantum analysis of black hole formation.

Abstract

We derive a partially gauge fixed Hamiltonian for black hole formation via real scalar field collapse. The class of models considered includes many theories of physical interest, including spherically symmetric black holes in $D$ spacetime dimensions. The boundary and gauge fixing conditions are chosen to be consistent with generalized Painleve-Gullstrand coordinates, in which the metric is regular across the black hole future horizon. The resulting Hamiltonian is remarkably simple and we argue that it provides a good starting point for studying the quantum dynamics of black hole formation.