Weak Cosmic Censorship and Weak Gravity Conjectures in CFT Thermodynamics

TL;DR

This paper investigates the relationship between the weak gravity conjecture and weak cosmic censorship in the thermodynamics of charged AdS black holes within conformal field theory, revealing conditions for their mutual consistency.

Contribution

It analyzes the interplay of WGC and WCCC in black hole thermodynamics, highlighting the roles of dark matter parameters and phase space in their validation.

Findings

WGC is supported at black hole critical points.

WCCC remains valid at critical junctures.

CFT thermodynamics shows greater WGC compatibility range.

Abstract

In this paper, we explore the intriguing interplay between fundamental theoretical physics concepts within the context of charged black holes. Specifically, we focus on the consistency of the weak gravity conjecture (WGC) and weak cosmic censorship conjecture (WCCC) in the thermodynamics of conformal field theory (CFT), and restricted phase space thermodynamics (RPST) for AdS Reissner-Nordstrom black holes with a perfect fluid dark matter (RN-PFDM). The WGC ensures that gravity remains the weakest force in the system. Meanwhile, the WCCC addresses the cosmic censorship problem by preventing the violation of fundamental physical laws near the black hole singularity. First, we analyze the RN black hole's free energy in both spaces, revealing a distinctive swallowtail pattern indicative of a first-order phase transition when certain free parameter conditions are met. We explore the WGC across different phase spaces, emphasizing the need for certain conditions in extended phase space thermodynamics (EPST), RPST, and CFT. We demonstrate that PFDM parameter \( \gamma \) and the radius of AdS \( l \) have a vital role in proving the satisfaction of the WGC. Also, these values have a linear relation with the range compatibility of WGC. The range of compatibility for WGC in RPST and EPST is the same while for CFT, this range is larger than EPST, and RPST. It means somehow the WGC and CFT are more consistent. The WCCC was examined at the critical juncture, confirming its validity in critical points. We conclude that the WGC is supported at the critical point of black holes, and the WCCC is also maintained, demonstrating the robustness of these conjectures within the critical ranges of black hole parameters