Isolated horizons: a generalization of black hole mechanics

A set of boundary conditions defining a non-rotating isolated horizon are given in Einstein-Maxwell theory. A spacetime 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-Nordström solutions. Finally, using these definitions, the zeroth and first laws of black hole mechanics are established for isolated horizons.