# Thermodynamics and weak cosmic censorship conjecture in the Kerr-AdS black hole

## TL;DR

This paper examines the thermodynamic laws and weak cosmic censorship conjecture in Kerr-AdS black holes, revealing their validity in different phase spaces and how they depend on specific parameters.

## Contribution

It provides a detailed analysis of thermodynamic laws and cosmic censorship in Kerr-AdS black holes, highlighting differences between normal and extended phase spaces.

## Key findings

- First law and cosmic censorship hold in all states in normal phase space.
- Second law validity depends on spin parameter and AdS radius in extended phase space.
- Extremal and near-extremal black holes remain unchanged after fermion absorption.

## Abstract

We investigate the laws of thermodynamics and weak cosmic censorship conjecture in the normal and extended phase space of a Kerr-AdS black hole by analyzing the energy-momentum relation of the absorbed fermion dropping into the horizon. In the normal phase space, the first law, second law as well as the weak cosmic censorship conjecture are found to be valid in all the initial states of the black hole. However, in the extended phase space, although the first law and weak cosmic censorship conjecture are still valid, the second law becomes more subtle. We find that the validity or violation of the second law depends on the spin parameter, the radius of the AdS spacetime, and their variations. In addition, in the extended phase space, the configurations of the extremal and near-extremal Kerr-AdS black holes are unchanged as the fermions are absorbed since the final and initial states are the same.