October 2014 Black Hole Thermodynamics S. Carlip∗ Department of Physics University of California Davis, CA 95616 USA Abstract The discovery in the early 1970s that black holes radiate as black bodies has radically affected our understanding of general relativity, and offered us some early hints about the nature of quantum gravity. In this chapter I will review the discovery of black hole thermodynamics and summarize the many indepen- dent ways of obtaining the thermodynamic and (perhaps) statistical mechanical properties of black holes. I will then describe some of the remaining puzzles, including the nature of the quantum microstates, the problem of universality, and the information loss paradox. arXiv:1410.1486v2 [gr-qc] 26 Aug 2015 ∗email:
[email protected] 1 Introduction The surprising discovery that black holes behave as thermodynamic objects has radically affected our understanding of general relativity and its relationship to quantum field theory. In the early 1970s, Bekenstein [1, 2] and Hawking [3, 4] showed that black holes radiate as black bodies, with characteristic temperatures and entropies ~κ Ahor kTH = ;SBH = ; (1.1) 2π 4~G where κ is the surface gravity and Ahor is the area of the horizon. These quantities appear to be inherently quantum gravitational, in the sense that they depend on both Planck's constant ~ and Newton's constant G. The resulting black body radiation, Hawking radiation, has not yet been directly observed: the temperature of an astrophysical black hole is on the order of a microkelvin, far lower than the cosmic microwave background temperature. But the Hawking temperature and the Bekenstein-Hawking entropy have been derived in so many independent ways, in different settings and with different assumptions, that it seems extraordinarily unlikely that they are not real.