Black Hole Mechanics

Abstract

Over the last thirty years, black holes have been shown to have a number of surprising properties. These discoveries have revealed unforeseen relations between the otherwise distinct areas of general relativity, quantum physics and statistical mechanics. This interplay, in turn, led to a number of deep puzzles at the very foundations of physics. Some have been resolved while others continue to baffle physicists. The starting point of these fascinating developments was the discovery of laws of black hole mechanics by Bardeen, Bekenstein, Carter and Hawking. They dictate the behavior of black holes in equilibrium, under small perturbations away from equilibrium, and in fully dynamical situations. While they are consequences of classical general relativity alone, they have a close similarity with the laws of thermodynamics. The origin of this seemingly strange coincidence lies in quantum physics. For further discussion, see articles on quantum field theory in curved space-times and quantum gravity. The focus of this review is just on black hole mechanics. The discussion is divided into three parts. In the first, we will introduce the notions of event horizons and black hole regions and discuss properties of globally stationary black holes. In the second, we will consider black holes which are themselves in equilibrium but in surroundings which may be time-dependent. Finally, in the third part, we summarize what is known in the fully dynamical situations. For simplicity, all manifolds and field are assumed to be smooth and, unless otherwise stated, space-time is assumed to be 4dimensional, with a metric of signature -,+,+,+, and the cosmological constant is