The semiclassical approximation is studied on hypersurfaces approaching the union of future null infinity and the event horizon on a large class of four-dimensional black hole backgrounds. Quantum fluctuations in the background geometry are shown to lead to a breakdown of the semiclassical approximation in these models. The boundary of the region where the semiclassical approximation breaks down is used to define a 'stretched horizon'. It is shown that the same effect that brings about the breakdown in semiclassical evolution associates a temperature and an entropy to the region behind the stretched horizon, and identifies the microstates that underlie the thermodynamical properties. The temperature defined in this way is equal to that of the black hole and the entropy is equal to the Bekenstein entropy up to a factor of order one.
Bibliographical noteFunding Information:
G.L. would like to thank Adi Stern for many helpful discussionsa nd the Center for TheoreticaPl hysics,MIT for financial supportd uringthe first stageso f this work.
The classical behaviour of black holes contains a number of features that appear to be in close analogy with the laws of thermodynamics: The existence of an irreducible *This work was supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under cooperative agreement DE-FC02-94ER408 ! 8, by the National Science Foundation under grants PHY-931581 I and PHY-9108311, and by the European Community Human Capital Mobility programme. l E-mail: email@example.com 2 Present address: Blackett Laboratory, Imperial College, Prince Consort Road, London SW7 2BZ, UK. E-mail: firstname.lastname@example.org
- Black hole
- Stretched horizon
ASJC Scopus subject areas
- Nuclear and High Energy Physics