Black holes, entropy, and information
Gary T. Horowitz · Cambridge University Press eBooks · 2011
Black holes are a continuing source of mystery. Although their classical properties have been understood since the 1970's, their quantum properties raise some of the deepest questions in theoretical physics. Some of these questions have recently been answered using string theory. I will review these fundamental questions, and the aspects of string theory needed to answer them. I will then explain the recent developments and new insights into black holes that they provide. Some remaining puzzles are mentioned in the conclusion. Introduction General properties of black holes were studied extensively in the early 1970's, and the basic theory was developed. One of the key results was Hawking's proof that the area of a black hole cannot decrease (Hawking 1971). This led Bekenstein (1973) to suggest that a black hole should have an entropy proportional to its horizon area. This suggestion of a connection between black holes and thermodynamics was strengthened by the formulation of the laws of black-hole mechanics (Bardeen et al. 1973). In addition to the total mass M , angular momentum J , and horizon area A of the black holes, these laws are formulated in terms of the angular velocity of the horizon Ω, and its surface gravity k . Recall that the surface gravity is the force at infinity required to hold a unit mass stationary near the horizon of a black hole.