# The weak cosmic censorship conjecture and thermodynamics in the quintessence AdS black hole under charge particle absorption

## TL;DR

This paper investigates the thermodynamics and weak cosmic censorship conjecture in quintessence AdS black holes during charged particle absorption, revealing conditions under which the laws hold or are violated, especially for extremal and near-extremal black holes.

## Contribution

It analyzes the validity of thermodynamic laws and cosmic censorship in quintessence AdS black holes, highlighting potential violations in extended phase space for near-extremal cases.

## Key findings

- First law of thermodynamics holds during particle absorption.
- Second law is violated for extremal and near-extremal black holes.
- Cosmic censorship can be violated for near-extremal black holes in extended phase space.

## Abstract

Considering the cosmological constant as the pressure, we mainly study the laws of thermodynamics and weak cosmic censorship conjecture in the Reissner-Nordstr\"{o}m-AdS black hole surrounded by quintessence dark energy under charged particle absorption. The first law of thermodynamics is found to be valid as a particle is absorbed by the black hole. The second law however is found to be violated for the extremal and near-extremal black holes since the entropy of these black hole decrease. Moreover, we find that the extremal black hole do not change it configuration in the extended phase space, implying that the weak cosmic censorship conjecture is valid. Remarkably, the near-extremal black hole can be overcharged beyond the extremal condition under charged particle absorption. That is, the cosmic censorship conjecture could be violated for the near-extremal black hole in the extended phase space. To make a comparison, we also discuss the first law, second law as well as the weak cosmic censorship conjecture in the normal phase space, and find that all of them are valid in this case.