Does black-hole entropy make sense?
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Bekenstein and Hawking saved the second law of thermodynamics near a black hole by assigning to the hole an entropySh proportional to the area of its event horizon. It is tempting to assume thatSh possesses all the features commonly associated with the physical entropy. Kundt has shown, however, thatSh violates several reasonable physical expectations. We review his criticism, augmenting it as follows: (a)Sh is a badly behaved state function requiring knowledge of the hole's future history; and (b) close analogs of event horizons in other space-times do not possess an “entropy.” We also discuss these questions: (c) IsSh suitable for all regions of a black-hole space-time? And (b) shouldSh be attributed to the exterior of a white hole? One can retainSh for the interior (respectively, exterior) of a black (respectively, white) hole, but we reject this as contrary to the information-theoretic derivation of horizon entropy given by Bekenstein. The total entropy defined by Kundt (all ordinary entropy on space-section cutting through the hole, no horizon term) and that of Bekenstein-Hawking (ordinary entropy outside horizon plus horizon term) appear to be complementary concepts with separate domains of validity. In the most natural choice, an observer inside a black hole will use Kundt's entropy, and one remaining outside that of Bekenstein-Hawking.
KeywordsEntropy Black Hole Differential Geometry Event Horizon State Function
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