Isolated horizons: Hamiltonian evolution and the first law

Abhay Ashtekar, Stephen Fairhurst, and Badri Krishnan
Phys. Rev. D 62, 104025 – Published 27 October 2000
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Abstract

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 nontrivial 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 nonrotating 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.

  • Received 24 May 2000

DOI:https://doi.org/10.1103/PhysRevD.62.104025

©2000 American Physical Society

Authors & Affiliations

Abhay Ashtekar*

  • Center for Gravitational Physics and Geometry, Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802
  • Institute for Theoretical Physics, University of California, Santa Barbara, California 93106

Stephen Fairhurst and Badri Krishnan

  • Center for Gravitational Physics and Geometry, Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802

  • *Email address: ashtekar@gravity.phys.psu.edu
  • Email address: fairhurs@phys.psu.edu
  • Email address: krishnan@phys.psu.edu

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Vol. 62, Iss. 10 — 15 November 2000

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