Further evidence for the weak gravity -- cosmic censorship connection

TL;DR

This work deepens the link between quantum gravity consistency (the weak gravity conjecture) and weak cosmic censorship in AdS by testing two generalizations of the electromagnetic setup: a dilaton coupling and an additional Maxwell field. Across these generalizations, a modified weak gravity bound—adjusted for the dilaton or for multiple charges—continues to prevent naked-curvature exposures, as shown by linear stability analyses and nonlinear DeTurck-based numerics for zero-temperature, boundary-driven configurations. The results demonstrate that the WGC bound is not only sufficient but often necessary to avoid censorship violations, even in rich multi-field setups, suggesting a profound connection between quantum gravity constraints and the preservation of cosmic censorship. The findings hint that quantum gravity may play a protective role in shielding bulk singularities from asymptotic observers, with potential implications for how extremal configurations decay in AdS/CFT contexts.

Abstract

We have recently shown that a class of counterexamples to (weak) cosmic censorship in anti-de Sitter spacetime is removed if the weak gravity conjecture holds. Surprisingly, the minimum value of the charge to mass ratio necessary to preserve cosmic censorship is precisely the weak gravity bound. To further explore this mysterious connection, we investigate two generalizations: adding a dilaton or an additional Maxwell field. Analogous counterexamples to cosmic censorship are found in these theories if there is no charged matter. Even though the weak gravity bound is modified, we show that in each case it is sufficient to remove these counterexamples. In most cases it is also necessary.

Figures (12)

• Figure 1: Logarithmic plot of the maximum of the Kretschmann scalar, over the whole spacetime, as a function of the boundary amplitude $a$ for $\alpha=1$. Different values of $\alpha$ show a similar qualitative behaviour. The red dashed line denotes the curvature of pure AdS.
• Figure 2: $a_{\max}$ as a function of $\alpha$: increasing $\alpha$ decreases $a_{\max}$.
• Figure 3: Minimal charge $q$ for condensing $\Phi$ as a function of the boundary amplitude $a$ for several values of the dilaton coupling $\alpha$, which are labelled on the right.
• Figure 4: Central value of expectation value of the operator dual to $\Phi$ as a function of the boundary amplitude $a$ for $\alpha = \sqrt{3}$. The condensation occurs around $a\sim 3.33$, in accordance with the linear results. There is no maximum amplitude.
• Figure 5: For $\alpha <1$, the bound on $q/\Delta$ needed to preserve cosmic censorship is precisely the weak gravity bound: the blue solid line indicates the onset of solutions with $\Phi\neq0$, and the red dots show the approximate location of singular solutions. On the left plot we have $\alpha=1/\sqrt{3}$ and on the right $\alpha = 0.9$. Notice the different scale on the horizontal axes. In both cases, $\Delta = 2$.