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.