Thermal fields, entropy and black holes

In this review we describe the statistical mechanics of quantum systems in the presence of a Killing horizon and compare statistical-mechanical and 1-loop contributions to black-hole entropy. The study of these questions was motivated by attempts to explain the entropy of black holes as a statistical-mechanical entropy of quantum fields propagating near the black-hole horizon. We provide an introduction to this field of research and review its results. In particular, we discuss the relation between the statistical-mechanical entropy of quantum fields and the Bekenstein-Hawking entropy in the standard scheme with renormalization of gravitational coupling constants and in the theories of induced gravity.