Isolated Horizons: A Generalization of Black Hole Mechanics

Abstract

A set of boundary conditions defining a non-rotating isolated horizon are given in Einstein-Maxwell theory. A space-time representing a black hole which itself is in equilibrium but whose exterior contains radiation admits such a horizon . Physically motivated, (quasi-)local definitions of the mass and surface gravity of an isolated horizon are introduced. Although these definitions do not refer to infinity, the quantities assume their standard values in Reissner-Nordstrom solutions. Finally, using these definitions, the zeroth and first laws of black hole mechanics are established for isolated horizons.

Figures (1)

• Figure 1: (a) A typical gravitational collapse. The portion $\Delta$ of the horizon at late times is isolated. The space-time $\mathcal{M}$ of interest is the triangular region bounded by $\Delta$, $\mathfs {I}^+$ and a partial Cauchy slice $M$. (b) Space-time diagram of a black hole which is initially in equilibrium, absorbs a small amount of radiation, and again settles down to equilibrium. Portions $\Delta_1$ and $\Delta_2$ of the horizon are isolated.