# Weak cosmic censorship conjecture with pressure and volume in the Gauss-Bonnet AdS black hole

## TL;DR

This paper investigates the validity of the weak cosmic censorship conjecture and thermodynamic laws in Gauss-Bonnet AdS black holes when considering pressure and volume, revealing conditions under which these principles hold or are violated.

## Contribution

It analyzes the weak cosmic censorship conjecture and thermodynamic laws in both normal and extended phase spaces for Gauss-Bonnet AdS black holes, including effects of particle absorption.

## Key findings

- First law and weak cosmic censorship hold in normal phase space.
- Second law is violated for extremal and near-extremal black holes in extended phase space.
- Near-extremal black holes' configuration changes after particle absorption.

## Abstract

With the Hamilton-Jacobi equation, we obtain the energy-momentum relation of a charged particle as it is absorbed by the Gauss-Bonnet AdS black hole. On the basis of the energy-momentum relation at the event horizon, we investigate the first law, second law, and weak cosmic censorship conjecture in both the normal phase space and extended phase space. Our results show that the first law, second law as well as the weak cosmic censorship conjecture are valid in the normal phase space for all the initial states are black holes. However, in the extended phase space, the second law is violated for the extremal and near-extremal black holes, and the weak cosmic censorship conjecture is violable for the near-extremal black hole, though the first law is still valid. In addition, in both the the normal and extended phase spaces, we find the absorbed particle changes the configuration of the near-extremal black hole, while don't change that of the extremal black hole.