Cosmic censorship hypothesis and entropy bound on black holes in a canonical ensemble

TL;DR

This paper demonstrates that the weak cosmic censorship hypothesis implies a universal entropy bound for black holes in a canonical ensemble, establishing a relationship between temperature and entropy and supporting the hypothesis.

Contribution

It provides mathematical proofs for static and stationary-axisymmetric black holes with reflection symmetry, establishing a universal temperature-entropy bound and supporting cosmic censorship.

Findings

Schwarzschild black hole has maximal entropy at fixed temperature.

Universal temperature-entropy bound for various black holes.

Supports weak cosmic censorship hypothesis.

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.