Testing the Weak Gravity -- Cosmic Censorship Connection

TL;DR

This paper investigates whether the weak gravity conjecture (WGC) can safeguard cosmic censorship (CC) in four-dimensional AdS by adding a charged scalar to Einstein–Maxwell–Λ theory. Through zero-mode analysis and construction of nonlinear charged-scalar hair, the authors show that a charged scalar with sufficient charge destabilizes the proposed CC counterexamples, preventing unbounded curvature growth; remarkably, the critical charge coincides with the AdS WGC bound $q_W=\Delta/L$. They further demonstrate that while hairy solutions exist beyond the previous CC-violating regime, lowering the charge toward below $q_W$ can reintroduce singularities, with the threshold approaching $q_W$ as the amplitude grows, indicating a tight (and in this class, precise) connection between CC and WGC. The work also discusses caveats concerning CC violations without Maxwell fields and emphasizes the need for time-dependent evolution to fully confirm the dynamical outcomes and end-states of the system.

Abstract

A surprising connection between the weak gravity conjecture and cosmic censorship has recently been proposed. In particular, it was argued that a promising class of counterexamples to cosmic censorship in four-dimensional Einstein-Maxwell-$Λ$ theory would be removed if charged particles (with sufficient charge) were present. We test this idea and find that indeed if the weak gravity conjecture is true, one cannot violate cosmic censorship this way. Remarkably, the minimum value of charge required to preserve cosmic censorship appears to agree precisely with that proposed by the weak gravity conjecture.

Figures (8)

• Figure 1: The minimum charge, $q_{\min}$, needed for a zero-mode as a function of the amplitude $a$, plotted for several different profiles. From bottom to top we have $n=2\,,4\,,6\,,8\,,10$, respectively. The horizontal dashed line represents the weak gravity bound $q_{\min}/q_W=1$. These curves were determined for $\Delta=2$.
• Figure 2: Similar to Fig. 1, but now for $\Delta=4$.
• Figure 3: The lowest quasinormal mode frequency for $n=8$, $\Delta = 4$, and $q=q_W$. The black dot denotes the zero-mode computed directly from Eq. (\ref{['eq:eige']}). The red dots have the opposite sign of $\omega$ from the blue dots. The insert on the right plots the data on a logarithmic scale, clearly showing that $\mathrm{Im} \ \omega$ becomes positive after the zero-mode, so the solution without the scalar field becomes unstable.
• Figure 4: $q_{\min}/q_W$ as a function of $\Delta\geq1$ plotted for $n=8$ and $a=a_{\max}$. The orange region indicates the region of moduli space where we used alternative boundary conditions.
• Figure 5: $\langle \mathcal{O}_2 \rangle$ as a function of $r$, for several values of $a$ and with $n=8$; from top to bottom we have $a= 10\,, 9.0\,, 8.0\,, 7.0\,,6.27$.