Dirty black holes: Entropy as a surface term

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Abstract
It is by now clear that the naive rule for the entropy of a black hole, (entropy)=1/4 (area of event horizon), is violated in many interesting cases. Indeed, several authors have recently conjectured that in general the entropy of a dirty black hole might be given purely in terms of some surface integral over the event horizon of that black hole. A formal proof of this conjecture, using Lorentzian signature techniques, has recently been provided by Wald. This paper performs two functions. First, by extending a previous analysis due to the present author [Phys. Rev. D 48, 583 (1993)] it is possible to provide a rather different proof of this result—a proof based on Euclidean signature techniques.
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