Mechanics of Isolated Horizons

TL;DR

This paper defines and analyzes the properties of isolated horizons in general relativity, establishing laws of black hole mechanics without relying on asymptotic infinity, applicable to various horizon types.

Contribution

It introduces local definitions of mass and surface gravity for isolated horizons and proves the zeroth and first laws of black hole mechanics in this context.

Findings

Local mass and surface gravity are well-defined for isolated horizons.

The zeroth and first laws of black hole mechanics are established for these horizons.

Definitions recover standard values in static black hole solutions.

Abstract

A set of boundary conditions defining an undistorted, non-rotating isolated horizon are specified in general relativity. A space-time representing a black hole which is itself in equilibrium but whose exterior contains radiation admits such a horizon. However, the definition is applicable in a more general context, such as cosmological horizons. Physically motivated, (quasi-)local definitions of the mass and surface gravity of an isolated horizon are introduced and their properties analyzed. Although their definitions do not refer to infinity, these quantities assume their standard values in the static black hole solutions. Finally, using these definitions, the zeroth and first laws of black hole mechanics are established for isolated horizons.