Cosmic-Quantum Connections: Assessing the Viability of Weak Gravity and Weak Cosmic Censorship Conjectures in Kerr-Newman-Kiselev-Letelier Black Hole

TL;DR

This paper investigates the compatibility of the weak gravity conjecture and weak cosmic censorship conjecture within a complex Kerr-Newman-Kiselev-Letelier black hole, showing that specific parameters can reconcile these fundamental ideas in quantum gravity.

Contribution

It demonstrates that the WGC and WCCC can be compatible in certain parameter regions of the KNKL black hole, establishing a bridge between quantum and cosmic considerations.

Findings

Presence of parameters ensures black hole horizons and prevents naked singularities.

Certain parameter ranges make both conjectures simultaneously valid.

Without these parameters, the black hole may violate the WCCC by exposing singularities.

Abstract

This paper addresses a potential validation of the weak gravity conjecture (WGC) with the weak cosmic censorship conjecture (WCCC), as a significant challenge in quantum gravity. We explore the viability of the WGC and WCCC in the context of the Kerr-Newman-Kiselev-Letelier (KNKL) black hole. Although these conjectures appear unrelated, but surprising connection between these conjectures, It establishes a bridge between the quantum and the cosmic. By imposing specific constraints on the black hole's parameters, we demonstrate that the WGC and WCCC can be compatible in certain regions. We examine the properties of the KNKL black hole for $q/m > (Q/M )_{ext}$, where $(Q/M )_{ext}$ is the charge-to-mass ratio of a large extremal black hole. We present figures to test the validity of both conjectures simultaneously. Without the spin parameter \(a\), the cloud of string parameter \(b\), quintessence parameter \(\gamma\), and equation of state parameter \(\omega\), the black hole either has two event horizons if \(Q^2/M^2 \leq 1\) or none event horizon if \(Q^2/M^2 > 1\) which leads to a naked singularity that contradicts the WCCC. However, when \(a\), \(b\), \(\gamma\), and \(\omega\) are present, the black hole has event horizons in some regions in the \(Q^2/M^2 > 1\) that ensure the singularity is covered and both the WGC and WCCC are fulfilled. Actually, we face this issue in the extremality state of the black hole viz these conjectures remain viable, with the black hole maintaining an event horizon. We conclude that certain regions of \(a\), \(b\), \(\gamma\), and \(\omega\) parameters can make the WGC and WCCC compatible, indicating their agreement when these parameters are present.