Does black-hole entropy make sense?

Abstract

Bekenstein and Hawking saved the second law of thermodynamics near a black hole by assigning to the hole an entropy Sh proportional to the area of its event horizon. It is tempting to assume that Sh possesses all the features commonly associated with the physical entropy. Kundt has shown, however, that Sh 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) Is Sh suitable for all regions of a black-hole space-time? And (b) should Sh be attributed to the exterior of a white hole? One can retain Sh 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. © 1979 Plenum Publishing Corporation.