Hawking and Unruh Radiation

Abstract

We saw that there are striking similarities between thermodynamics and black hole mechanics as summarized in (Wald, University of Chicago Press, 2010, [8]). These were considered by many to be mere surface similarities, until Hawking showed that semiclassical black holes emit thermal radiation at inverse temperature $\beta = \frac{2\pi }{\kappa }$ (Hawking, Commun Math Phys, 43:199–220, 1975, [9]). That is, black holes seem to be truly thermodynamic objects which radiate at a well-defined temperature. However, this immediately poses a problem, as thermal radiation is in a mixed quantum state, which means we need a density matrix to describe it. Hence, if a black hole formed out of a pure state evaporates into mixed thermal radiation, we have a pure-to-mixed state transition, which violates the unitarity postulate of quantum mechanics. There thus seems to be a conflict between quantum mechanics and general relativity, which presents perhaps the most important unsolved problem of contemporary theoretical physics. The remaining sections will look at the origin of this problem as well as some partial solutions that have been proposed thus far.