# Thermodynamics and weak cosmic censorship conjecture of the BTZ black holes in the extended phase space

## TL;DR

This paper investigates the thermodynamic laws and weak cosmic censorship conjecture for BTZ black holes during fermion absorption, analyzing differences between normal and extended phase spaces with regard to stability and law validity.

## Contribution

It examines the validity of thermodynamic laws and cosmic censorship in both phase spaces, highlighting the role of the renormalization energy in the extended phase space.

## Key findings

- First and second laws hold in normal phase space.
- First law and censorship conjecture hold in extended phase space.
- Extremal black holes remain stable in extended phase space.

## Abstract

As charged fermions drop into the BTZ black holes, we check the laws of thermodynamics and weak cosmic censorship conjecture in the normal phase space and extended phase space, where the cosmological parameter and renormalization length are regarded as extensive quantities. In the normal phase space, the first and second law of thermodynamics as well as the weak cosmic censorship are valid. While in the extended phase space, though the first law and weakcosmic censorship conjecture are still valid, the second law is dependent on the variation of the renormalization energy $dK$. In addition, in the extended phase space, the configurations of the extremal and near-extremal black holes will not be changed for they are stable while in the normal phase space, the extremal and near-extremal black holes will evolve into non-extremal black holes.