# Minimal Length Effect on Thermodynamics and Weak Cosmic Censorship Conjecture in anti-de Sitter Black Holes via Charged Particle Absorption

## TL;DR

This study explores how minimal length effects, modeled via the generalized uncertainty principle, influence the thermodynamics and weak cosmic censorship conjecture in charged AdS black holes during particle absorption, revealing conditions under which laws hold or break down.

## Contribution

It introduces the impact of minimal length effects on black hole thermodynamics and censorship conjecture using GUP, extending analysis to both normal and extended phase spaces.

## Key findings

- Minimal length accelerates entropy increase in normal phase space.
- Second law of thermodynamics can be violated in extended phase space under certain conditions.
- Weak cosmic censorship conjecture remains valid in GUP deformed cases for extremal and near-extremal black holes.

## Abstract

In this paper, we investigate minimal length effects on the thermodynamics and weak cosmic censorship conjecture in a RN-AdS black bole via charged particle absorption. We first use the generalized uncertainty principle (GUP) to investigate the minimal length effect on the Hamilton-Jacobi equation. After the deformed Hamilton-Jacobi equation is derived, we use it to study the variations of the thermodynamic quantities of a RN-Ads black hole via absorbing a charged practice. Furthermore, we check the second law of thermodynamics and the weak cosmic censorship conjecture in two phase spaces. In the normal phase space, the second law of thermodynamics and the weak cosmic censorship conjecture are satisfied in the usual and GUP deformed cases, and the minimal length effect makes the increase of entropy faster than the usual case. After the charge particle absorption, the extremal RN-AdS black hole becomes non-extremal. In the extended phase space, the black hole entropy can either increase or decrease. When $T>2Pr_{+}$, the second law is satisfied. When $T<2Pr_{+}$, the second law of thermodynamics is violated for the extremal or near-extremal black hole. Finally, we find that the weak cosmic censorship conjecture is legal for extremal and near-extremal RN-Ads black holes in the GUP deformed case.