# Thermodynamics and weak cosmic censorship conjecture of the torus-like black hole

## TL;DR

This paper investigates the thermodynamic laws and weak cosmic censorship conjecture in torus-like black holes, finding that the first law and censorship hold universally, while the second law's validity depends on the phase space.

## Contribution

It demonstrates the phase space independence of the weak cosmic censorship conjecture and the first law of thermodynamics in torus-like black holes.

## Key findings

- First law of thermodynamics holds in both phase spaces.
- Weak cosmic censorship conjecture is valid regardless of phase space.
- Second law of thermodynamics is only valid in normal phase space.

## Abstract

After studying the energy-momentum relation of charged particles' Hamilton-Jacobi equations, we discuss the laws of thermodynamics and the weak cosmic censorship conjecture in torus-like black holes. We find that both the first law of thermodynamic as well as the weak cosmic censorship conjecture are valid in both the normal phase space and extended phase space. However, the second law of thermodynamics is only valid in the normal phase space. Our results show that the first law and weak cosmic censorship conjecture do not depend on the phase spaces while the second law depends. What's more, we find that the shift of the metric function that determines the event horizon take the same form in different phase spaces, indicating that the weak cosmic censorship conjecture is independent of the phase space.