Isolated Horizons in 2+1 Gravity

Details Isolated Horizons in 2+1 Gravity Isolated Horizons in 2+1 Gravity

2002-06-09

arxiv.org/abs/gr-qc/0206024v3

Adv.Theor.Math.Phys. 6 (2002) 507-555

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27 pages, 1 figure, revtex 4; v.2: figure improved, references added, typos corrected; v.3: 49 pages, ATMP style, "Vacuum spac

Scientific paper

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.

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