Isolated horizons in 2 + 1 gravity

Abhay Ashtekar, Olaf Dreyer, Jacek Wiśniewski

Research output: Contribution to journalArticlepeer-review

62 Scopus citations


Using ideas employed in higher dimensional gravity, non-expanding, weakly isolated and isolated horizons are introduced and analyzed in 2+1 dimensions. While the basic definitions can be taken over directly from higher dimensions, their consequences are somewhat different because of the peculiarities associated with 2+1 dimensions. Nonetheless, as in higher dimensions, we are able to: i) analyze the horizon geometry in detail; ii) introduce the notions of mass, charge and angular momentum of isolated horizons using geometric methods; and, iii) generalize the zeroth and the first laws of black hole mechanics. The Hamiltonian methods also provide, for the first time, expressions of total angular momentum and mass of charged, rotating black holes and their relation to the analogous quantities defined at the horizon. We also construct the analog of the Newman-Penrose framework in 2+1 dimensions which should be useful in a wide variety of problems in 2+1 dimensional gravity.

Original languageEnglish (US)
Pages (from-to)507-555
Number of pages49
JournalAdvances in Theoretical and Mathematical Physics
Issue number3
StatePublished - May 2002

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • General Physics and Astronomy


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