Entropy in the interior of a Kerr black hole

TL;DR

This paper introduces a new method to calculate the entropy of the interior volume of Kerr black holes, revealing its proportionality to Bekenstein-Hawking entropy and revisiting the black hole information paradox.

Contribution

A novel method for computing interior volume entropy of Kerr black holes, applicable to more general cases, and a revised proportionality coefficient between interior and horizon entropies.

Findings

Entropy of Kerr black hole interior is proportional to Bekenstein-Hawking entropy in early evaporation stages.

Recalculated entropy coefficient is half of previous estimates.

Discussed implications for the black hole information paradox.

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.