Local Hamiltonian for Spherically Symmetric Collapse: Geometrodynamics Approach

Understand

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.