Entropy in the interior of a Kerr black hole

Abstract

Christodoulou and Rovelli have shown that the maximal interior volume of a Schwarzschild black hole linearly grows with time. Recently, their conclusion has been extended to the Reissner{-}Nordstr$\ddot{\text{o}}$m and Kerr black holes. Meanwhile, the entropy of interior volume in a Schwarzschild black hole has also been calculated. Here, a new method calculating the entropy of interior volume of the black hole is given and it can be used in more general cases. Using this method, the entropy associated with the volume of a Kerr black hole is calculated and it is found that the entropy is proportional to the Bekenstein-Hawking entropy in the early stage of black hole evaporation. Using the differential form, the entropy of interior volume in a Schwarzschild black hole is recalculated. It is shown that the proportionality coefficient between the entropy and the Bekenstein-Hawking entropy is half of that given in the previous literature. Moreover, the black hole information paradox is brought up again and discussed.

arXiv comment16 pages, 3 figures

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• Interior Volume of Banados-Teitelboim-Zanelli Black Hole
• Volume dependent extension of Kerr-Newman black hole thermodynamics
• Information paradox and corrected thermodynamics for black holes
• The CR Volume for Black Holes and the Corresponding Entropy Variation: A Review
• Metric fluctuations in higher-dimensional black holes
• Information evolution in the interior of an axially symmetric BTZ black hole
• Evolution of interior entropy of a loop quantum-corrected black hole pierced by a cosmic string