Classical Black Holes Are Hot

In the early 1970s it is was realized that there is a striking formal analogy between the Laws of black-hole mechanics and the Laws of classical thermodynamics. Before the discovery of Hawking radiation, however, it was generally thought that the analogy was only formal, and did not reflect a deep connection between gravitational and thermodynamical phenomena. It is still commonly held that the surface gravity of a stationary black hole can be construed as a true physical temperature and its area as a true entropy only when quantum effects are taken into account; in the context of classical general relativity alone, one cannot cogently construe them so. Does the use of quantum field theory in curved spacetime offer the only hope for taking the analogy seriously? I think the answer is `no'. To attempt to justify that answer, I shall begin by arguing that the standard argument to the contrary is not physically well founded, and in any event begs the question. Looking at the various ways that the ideas of "temperature" and "entropy" enter classical thermodynamics then will suggest arguments that, I claim, show the analogy between classical black-hole mechanics and classical thermodynamics should be taken more seriously, without the need to rely on or invoke quantum mechanics. In particular, I construct an analogue of a Carnot cycle in which a black hole "couples" with an ordinary thermodynamical system in such a way that its surface gravity plays the role of temperature and its area that of entropy. Thus, the connection between classical general relativity and classical thermodynamics on their own is already deep and physically significant, independent of quantum mechanics.Comment: 30 pages; revised so as to address possible counter-example due to Bob Wald, that treating black holes purely classically may lead to violations of the GS

Similarities Between Classical Timelike Geodesics in a Naked Reissner-Nordstrom Singularity Background and the Behaviour of Electrons in Quantum Theory

It is generally assumed that naked singularities must be physically excluded, as they could otherwise introduce unpredictable influences in their future null cones. Considering geodesics for a naked Reissner-Nordstrom singularity, it is found that the singularity is effectively clothed by its repulsive nature. Regarding electron as naked singularity, the size of the clothed singularity (electron) turns out to be classical electro-magnetic radius of the electron, to an observer falling freely from infinity, initially at rest. The size shrinks for an observer falling freely from infinity, with a positive initial velocity. For geodetic parameters corresponding to negative energy there are trapped geodesics. The similarity of this picture with that arising in the Quantum Theory is discussed.Comment: 8 pages, 6 figure

Nonsingular 2-D Black Holes and Classical String Backgrounds

We study a string-inspired classical 2-D effective field theory with {\it nonsingular} black holes as well as Witten's black hole among its static solutions. By a dimensional reduction, the static solutions are related to the $(SL(2,R)_{k}\otimes U(1))/U(1)$ coset model, or more precisely its $O\bigl((\alpha')^{0}\bigr)$ approximation known as the 3-D charged black string. The 2-D effective action possesses a propagating degree of freedom, and the dynamics are highly nontrivial. A collapsing shell is shown to bounce into another universe without creating a curvature singularity on its path, and the potential instability of the Cauchy horizon is found to be irrelevent in that some of the infalling observers never approach the Cauchy horizon. Finally a $SL(2,R)_{k}/U(1)$ nonperturbative coset metric, found and advocated by R. Dijkgraaf et.al., is shown to be nonsingular and to coincide with one of the charged spacetimes found above. Implications of all these geometries are discussed in connection with black hole evaporation.Comment: 30 pages with 2 figures, harvmac, CALT-68-1852 (Discussions on the gravitational collapse of thin shells in a charged spacetime are clarified. Two extra references.