Isolated Horizons: Hamiltonian Evolution and the First Law

Details Isolated Horizons: Hamiltonian Evolution and the First Law Isolated Horizons: Hamiltonian Evolution and the First Law

2000-05-18

arxiv.org/abs/gr-qc/0005083v3

Phys.Rev. D62 (2000) 104025

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

56 pages, 1 figure, Revtex; Final Version, to appear in PRD

Scientific paper

10.1103/PhysRevD.62.104025

A framework was recently introduced to generalize black hole mechanics by replacing stationary event horizons with isolated horizons. That framework is significantly extended. The extension is non-trivial in that not only do the boundary conditions now allow the horizon to be distorted and rotating, but also the subsequent analysis is based on several new ingredients. Specifically, although the overall strategy is closely related to that in the previous work, the dynamical variables, the action principle and the Hamiltonian framework are all quite different. More importantly, in the non-rotating case, the first law is shown to arise as a necessary and sufficient condition for the existence of a consistent Hamiltonian evolution. Somewhat surprisingly, this consistency condition in turn leads to new predictions even for static black holes. To complement the previous work, the entire discussion is presented in terms of tetrads and associated (real) Lorentz connections.

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