# Thermodynamics and weak cosmic censorship conjecture in the charged RN-AdS black hole surrounded by quintessence under the scalar field

## TL;DR

This study investigates the thermodynamic behavior and the validity of the weak cosmic censorship conjecture for RN-AdS black holes surrounded by quintessence under scalar field scattering, revealing phase space-dependent thermodynamic laws.

## Contribution

It analyzes the thermodynamics and censorship conjecture in both extended and normal phase spaces, highlighting differences in thermodynamic law validity.

## Key findings

- First law holds in both phase spaces.
- Second law valid only in normal phase space.
- Weak cosmic censorship conjecture remains valid in both phases.

## Abstract

In this paper, we study the thermodynamics and the weak cosmic censorship conjecture of the RN-AdS black hole surrounded by the quintessence under the scattering of a charged complex scalar field. With scalar field scattering, the variation of the black hole is calculated in the extended and normal phase spaces. In the extended phase space, the cosmological constant and the normalization parameter are considered as thermodynamic variables, and the first law of thermodynamics is valid, but the second law of thermodynamics is not valid. In the normal phase space, the cosmological constant and the normalization parameter are fixed, and the first and second laws of thermodynamics can also be satisfied. Furthermore, the weak cosmic censorship conjecture is both valid in the extended and normal phase spaces.