Flat slice Hamiltonian formalism for dynamical black holes

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.

arXiv comment11 pages, refererences added, discussions clarified, version to appear in PRD

References in corpus (11)

• The Thermodynamics of Black Holes
• Gravity and the Thermodynamics of Horizons
• Geometrodynamics of Schwarzschild Black Holes
• Microscopic Formulation of Black Holes in String Theory
• Effect of Self-Interaction on Charged Black Hole Radiance
• Regular coordinate systems for Schwarzschild and other spherical spacetimes
• On Quantum Statistical Mechanics of a Schwarzschild Black Hole
• Reduced phase space formalism for spherically symmetric geometry with a massive dust shell
• Flat foliations of spherically symmetric geometries
• Note on flat foliations of spherically symmetric spacetimes
• Kruskal coordinates as canonical variables for Schwarzschild black holes

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