Regular Article - Theoretical Physics

Testing the weak cosmic censorship conjecture for a Reissner–Nordström–de Sitter black hole surrounded by perfect fluid dark matter

¹ Institute for Theoretical Physics and Cosmology, Zheijiang University of Technology, 310023, Hangzhou, China
² Ulugh Beg Astronomical Institute, Astronomicheskaya 33, 100052, Tashkent, Uzbekistan
³ National University of Uzbekistan, 100174, Tashkent, Uzbekistan
⁴ Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, Kori Niyoziy 39, 100000, Tashkent, Uzbekistan
⁵ Department of Mathematics, School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), H-12, 44000, Islamabad, Pakistan
⁶ Canadian Quantum Research Center, 204-3002 32 Ave, V1T 2L7, Vernon, BC, Canada

^c mjamil@zjut.edu.cn

Received: 19 July 2020
Accepted: 30 June 2021
Published online: 6 July 2021

Abstract

In this paper, we test the weak cosmic censorship conjecture (WCCC) for the Reissner–Nordström–de Sitter (RN-dS) black hole surrounded by perfect fluid dark matter. We consider a spherically symmetric perturbation on deriving linear and non-linear order perturbation inequalities by applying a new version of gedanken experiments well accepted from the work of Sorce and Wald. Contrary to the well-known result that the Reissner–Nordström (RN) black hole could be overcharged under linear order particle accretion it is hereby shown that the same black hole in perfect fluid dark matter with cosmological parameter cannot be overcharged. Considering a realistic scenario in which black holes cannot be considered to be in vacuum we investigate the contribution of dark matter and cosmological constant in the overcharging process of an electrically charged black hole. We demonstrate that the black hole can be overcharged only when two fields induced by dark matter and cosmological parameter are completely balanced. Further we present a remarkable result that a black hole cannot be overcharged beyond a certain threshold limit for which the effect arising from the cosmological constant dominates over the effect by the perfect fluid dark matter. Thus even for a linear accretion process, the black hole cannot always be overcharged and hence obeys the WCCC in general. This result would continue to be fulfilled for non-linear order accretion.