Isolated horizons: Hamiltonian evolution and the first law

Abhay Ashtekar, Stephen Fairhurst, Badri Krishnan

Research output: Contribution to journalArticlepeer-review

271 Scopus citations


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.

Original languageEnglish (US)
Article number104025
Pages (from-to)1-29
Number of pages29
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Issue number10
StatePublished - Nov 15 2000

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)


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