Local Hamiltonian for Spherically Symmetric Collapse: Geometrodynamics Approach

Details Local Hamiltonian for Spherically Symmetric Collapse: Geometrodynamics Approach Local Hamiltonian for Spherically Symmetric Collapse: Geometrodynamics Approach

2011-12-14

arxiv.org/abs/1112.3301v3

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

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.

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