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

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.