Local Hamiltonian for Spherically Symmetric Collapse: Geometrodynamics Approach

TL;DR

This paper derives a universal, simple local Hamiltonian for spherically symmetric gravitational collapse using geometrodynamics, applicable to various gravity theories including Lovelock gravity, clarifying the geometrical basis and broad applicability.

Contribution

It shows that a local Hamiltonian for spherically symmetric collapse can be derived from geometrodynamics for theories obeying Birkhoff's theorem, extending to multiple gravity models.

Findings

Derived a universal local Hamiltonian for spherically symmetric collapse.

Applicable to a wide class of gravity theories including Lovelock gravity.

Clarified the geometrical interpretation of the Hamiltonian.

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.