Testing the weak cosmic censorship conjecture for a Reissner-Nordstr\"{o}m-de Sitter black hole surrounded by perfect fluid dark matter

TL;DR

This study tests the weak cosmic censorship conjecture for Reissner-Nordström-de Sitter black holes surrounded by perfect fluid dark matter, showing that such black holes cannot be overcharged under realistic conditions, thus supporting the conjecture.

Contribution

The paper introduces a new analysis of black hole overcharging considering dark matter and cosmological constant effects, extending previous results to more realistic scenarios.

Findings

Black holes in perfect fluid dark matter cannot be overcharged under linear or non-linear accretion.

Overcharging occurs only when dark matter and cosmological effects are perfectly balanced.

A threshold exists beyond which the cosmological constant prevents overcharging, supporting the WCCC.

Abstract

In this paper, we test the weak cosmic censorship conjecture (WCCC) for the Reissner-Nordstr\"{o}m-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 new version of gedanken experiments well accepted from the work of Sorce and Wald. Contrary to the well-known result that the Reissner-Nordstr\"{o}m (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 can not 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 give a remarkable result that 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 linear accretion process, the black hole cannot always be overcharged and hence obeys the WCCC in general. This result would continues be fulfilled for non-linear order accretion.