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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
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