A conjectured inequality bounding black hole entropy by its specific heat is proven for a special static class and verified for many rotating and charged black holes.
Cosmic censorship hypothesis and entropy bound on black holes in a canonical ensemble
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abstract
This paper argues that the weak cosmic censorship hypothesis implies that the Schwarzschild black hole has maximal entropy in all stationary black holes of fixing temperature, or equivalently, to store a same amount of information the Schwarzschild black hole has highest temperature. It then gives the independent mathematical proofs for 4-dimensional general static black holes and stationary-axisymmetric black holes which have "$t$-$\phi$" reflection isometry. This result does not only provide a new universal bound between temperature and entropy of black holes but also offers us new evidence to support the weak cosmic censorship hypothesis.
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Black Hole Entropy Bounded by the Specific Heat
A conjectured inequality bounding black hole entropy by its specific heat is proven for a special static class and verified for many rotating and charged black holes.