Thermodynamics and Cosmic Censorship Conjecture in Kerr-Newman-de Sitter Black Hole.

Bogeun Gwak

doi:10.3390/e20110855

Abstract

We investigate the laws of thermodynamics and the validity of the cosmic censorship conjecture in the Kerr–Newman–de Sitter black hole under charged particle absorption. Here, the black hole undergoes infinitesimal changes because of the momenta carried by the particle entering it. The cosmic censorship conjecture is tested by whether the black hole can be overcharged beyond the extremal condition under absorption. The changes in the black hole violate the second law of thermodynamics. Furthermore, this is related to the cosmic censorship conjecture. To resolve this violation, we impose a reference energy of the particle at the asymptotic region based on the first law of thermodynamics. Under imposition of the reference energy, the absorption satisfies the laws of thermodynamics, and the extremal black hole cannot be overcharged. Thus, the cosmic censorship conjecture is valid under the absorption.

Highlights

The accelerated expansion of our universe as evidenced by the data obtained from cosmological evolution or supernovae [1,2,3] suggests the presence of a small positive cosmological constant in Einstein gravity
This paper is organized as follows: Section 2 introduces the Kerr–Newman–de Sitter (KNdS) black hole and its thermodynamic properties; Section 3 shows that under charged particle absorption, the equations of particle motion should be modified to satisfy the laws of thermodynamics, and we obtain the changes in the black hole in terms of the conserved quantities of the particle; Section 4 proves that the cosmic censorship conjecture is valid for an extremal KNdS black hole; and Section 5 briefly summarizes our results
We studied the laws of thermodynamics and found that the cosmic censorship conjecture is valid in the extremal KNdS black hole under charged particle absorption

Summary

Introduction

The accelerated expansion of our universe as evidenced by the data obtained from cosmological evolution or supernovae [1,2,3] suggests the presence of a small positive cosmological constant in Einstein gravity. We investigate the relation between the laws of thermodynamics and the cosmic censorship conjecture in the Kerr–Newman–de Sitter (KNdS) black hole under the condition of charged particle absorption. The cosmic censorship conjecture is valid for a four-dimensional black hole with a positive cosmological constant, provided that the laws of thermodynamics are satisfied. This paper is organized as follows: Section 2 introduces the KNdS black hole and its thermodynamic properties; Section 3 shows that under charged particle absorption, the equations of particle motion should be modified to satisfy the laws of thermodynamics, and we obtain the changes in the black hole in terms of the conserved quantities of the particle; Section 4 proves that the cosmic censorship conjecture is valid for an extremal KNdS black hole; and Section 5 briefly summarizes our results

Kerr–Newman–de Sitter Black Holes

Laws of Thermodynamics under Charged Particle Absorption

Validity of Cosmic Censorship Conjecture in Extremal Black Hole

Summary