Abstract
Bekenstein and Hawking saved the second law of thermodynamics near a black hole by assigning to the hole an entropyS h proportional to the area of its event horizon. It is tempting to assume thatS h possesses all the features commonly associated with the physical entropy. Kundt has shown, however, thatS h violates several reasonable physical expectations. We review his criticism, augmenting it as follows: (a)S h 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) IsS h suitable for all regions of a black-hole space-time? And (b) shouldS h be attributed to the exterior of a white hole? One can retainS h 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.
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Wilkins, D. Does black-hole entropy make sense?. Gen Relat Gravit 11, 45–58 (1979). https://doi.org/10.1007/BF00756671
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DOI: https://doi.org/10.1007/BF00756671