Local Hamiltonian for Spherically Symmetric Collapse: Geometrodynamics Approach

Abstract

Recently a {\it local} true (completely gauge fixed) Hamiltonian for spherically symmetric collapse was derived in terms of Ashtekar variables. We show that such a local Hamiltonian follows directly from the geometrodynamics of gravity theories that obey a Birkhoff theorem and possess a mass function that is constant on the constraint surface in vacuum. In addition to clarifying the geometrical content, our approach has the advantage that it can be directly applied to a large class of spherically symmetric and 2D gravity theories, including $p$-th order Lovelock gravity in D dimensions. The resulting expression for the true local Hamiltonian is universal and remarkably simple in form.

16 pages, no figures, final form to appear in Phys. Rev. D

References in corpus (6)

• Generalized Misner-Sharp quasi-local mass in Einstein-Gauss-Bonnet gravity
• Lovelock black holes with maximally symmetric horizons
• Hamiltonian Formulation of Scalar Field Collapse in Einstein Gauss Bonnet Gravity
• Loop Quantum Gravity and Cosmology: A dynamical introduction
• A local Hamiltonian for spherically symmetric gravity coupled to a scalar field
• A Partially Gauged Fixed Hamiltonian for Scalar Field Collapse

Cited by in corpus (1)

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