Isolated Horizons: A Generalization of Black Hole Mechanics

TL;DR

This paper introduces a framework for defining and analyzing isolated horizons in Einstein-Maxwell theory, establishing their physical properties and laws of black hole mechanics without relying on asymptotic infinity.

Contribution

It generalizes black hole mechanics to isolated horizons with local definitions of mass and surface gravity, applicable in non-stationary spacetimes.

Findings

Defined boundary conditions for non-rotating isolated horizons

Introduced local mass and surface gravity definitions

Proved zeroth and first laws for isolated horizons

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.