Abstract

In this paper, we investigate the minimal length effects on the thermodynamics and weak cosmic censorship conjecture in a RN-AdS black hole 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 particle. 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 nonextremal. 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.

Highlights

  • The classical theory of black holes predicts that nothing, including light, could escape from black holes

  • We investigated the minimal length effect on the weak cosmic censorship conjecture in a RN-AdS black bole via the charged particle absorption

  • We checked the second law of thermodynamics and the weak cosmic censorship conjecture in a RN-Ads black hole

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Summary

Introduction

The classical theory of black holes predicts that nothing, including light, could escape from black holes. The results showed that the first law of thermodynamics and the weak cosmic censorship conjecture are satisfied, while the second law of thermodynamics is violated for the extremal and nearextremal black holes [34,35,36,37,38,39,40,41,42,43]. We will discuss the effects of quantum gravity on black hole thermodynamics and the weak cosmic censorship conjecture in the framework of GUP.

Deformed Hamilton-Jacobi Equation in a RN-AdS Black Hole
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