Isolated Horizons in 2+1 Gravity

TL;DR

This paper extends the concepts of isolated horizons from higher dimensions to 2+1 gravity, analyzing their geometry, defining physical quantities, and generalizing black hole laws using geometric and Hamiltonian methods.

Contribution

It introduces isolated horizon concepts in 2+1 dimensions, adapting definitions and laws from higher dimensions, and provides new expressions for black hole mass and angular momentum.

Findings

Detailed analysis of horizon geometry in 2+1 dimensions

New geometric definitions of mass, charge, and angular momentum for isolated horizons

Expressions of total mass and angular momentum for charged, rotating black holes

Abstract

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.