# Thermodynamics and weak cosmic censorship conjecture in extended phase spaces of anti-de Sitter black holes with particles' absorption

## TL;DR

This paper investigates how particle absorption affects the thermodynamics and weak cosmic censorship conjecture in extended phase spaces of charged anti-de Sitter black holes within massive gravity, revealing violations of the second law in extremal cases.

## Contribution

It explores the impact of particle absorption on thermodynamics and cosmic censorship in extended phase spaces, including the violation of the second law for extremal black holes.

## Key findings

- Second law of thermodynamics is violated in extremal black holes.
- Near-extremal and extremal black holes remain near their extremity after particle absorption.
- The first law of thermodynamics is confirmed in the extended phase space context.

## Abstract

The thermodynamics and weak cosmic censorship conjecture in extended phase spaces of charged anti-de Sitter black holes describing the massive gravity are investigated by the absorptions of the scalar particle and fermion. The cosmological constant is seen as a pressure with a conjugate volume. The first law of thermodynamics is recovered. The second law of thermodynamics is violated in the extended phase space of the extremal black hole. For the near-extremal and extremal black holes, the validity of weak cosmic censorship conjecture is tested by evaluating the minimum values of the metric function $f$. It is found that they remain their near-extremity and extremity when the particles are absorbed.