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.