# Weak Cosmic Censorship with Pressure and Volume in Charged Anti-de Sitter Black Hole under Charged Scalar Field

## TL;DR

This paper examines the weak cosmic censorship conjecture in charged anti-de Sitter black holes with pressure and volume, analyzing the effects of charged scalar field scattering in various dimensions and its implications for thermodynamics and extremality.

## Contribution

It demonstrates that the weak cosmic censorship conjecture holds in these black holes despite violations of the second law of thermodynamics in extremal cases.

## Key findings

- Second law of thermodynamics is violated in extremal black holes.
- Weak cosmic censorship remains valid despite thermodynamic violations.
- Black hole extremality is invariant under scalar field scattering.

## Abstract

We investigate the weak cosmic censorship conjecture in charged anti-de Sitter black holes with thermodynamic pressure and volume by the scattering of the charged scalar field in four and higher dimensions. We assume that the internal energy and electric charge of the black hole changes infinitesimally according to the energy and charge fluxes of the scalar field. Then, found to be an isobaric process, the changes in the black hole can be well reproduced to the first law of thermodynamics, although we find that the second law of thermodynamics is violated in extremal and near-extremal black holes. Nevertheless, the weak cosmic censorship conjecture remains valid, because the extremality of a black hole is invariant despite changes in internal energy and electric charge.