Entropy Bounds for Rotating Systems and The Nine Souls of The Generalized Second Law

Black-hole physics mirrors thermodynamics in many respects. Inparticular, it is widely believed that a system consisting of ordinary matter interacting with a black hole will obey the generalized second law of thermodynamics. In this paper we challenge the validity of the law in a gedanken experiment in which an entropy-bearing rotating system falls into a stationary black hole. It is shown that the law is protected by the (apparently miraculous) upper bound imposed by nature on the (intrinsic) spins of the known fundamental massive particles. Furthermore, we derive a universal upper bound on the entropy of a rotating system. Remarkably, (all) Kerr black holes attain the bound. One of the most intriguing features of both the classical and quantum theory of blackholes is the striking analogy between the laws of black-hole physics and the universal laws of thermodynamics [1–6]. In particular, Hawking’s (classical) theorem [3]: “The surface area of a black hole never decreases” is a property reminiscent of the entropy of a closed system. This striking analogy had led Bekenstein [7–9] to conjecture that the area of a black hole (in suitable units) may be regarded as the black-hole entropy – entropy in the sense of information about the black-hole interior inaccessible to observers outside the black hole.