Jennie Traschen, University of Massachusetts
Black Holes and Thermodynamics


In 1971 Hawking published the Area Theorem, which shows that the area of a black hole either increases or stays the same.  Two years later, Bardeen, Carter, and Hawking proved a theorem which relates the changes in the mass of a black hole, to changes in its area.  These two results had a striking formal resemblance to the second and first laws of thermodynamics, respectively.  However, since nothing comes out of a black hole, it seemed that a black hole can not radiate, can not have a temperature, and so can not really be a thermodynamic system.  Then in 1975, Hawking calculated that black holes do indeed radiate quantum mechanical particles, in a black body spectrum, at temperature proportional to Planck’s constant.

Over the past thirty years, Hawking radiation has (almost) become a household word.  The lure of understanding the thermodynamics of black holes has fueled both physicists’ imaginations and calculations.  In this talk, we will aim to (1) explain the classical geometrical meaning of the mass, area, and surface gravity of a black hole, which are the quantities which appear in the first and second laws, and (2) present the main geometrical steps in Hawking’s calculation of black hole radiation.  The role of supersymmetric spacetimes in the spectrum of black branes will be discussed.  We will point out examples that fit into the standard lore, and ones that don’t.  As black hole evaporation has been an important clue in efforts to develop a quantum theory of gravity, the goal of the talk is to be an aid in evaluating progress in these efforts.