Evidence for an Electrifying Violation of Cosmic Censorship

TL;DR

Addressing whether cosmic censorship can fail in AdS, the paper analyzes Einstein-Maxwell theory with a localized boundary defect and AdS boundary conditions. It constructs static, nonzero-temperature solutions using the DeTurck method and reveals horizon deformations forming 'black mushrooms' with increasing boundary amplitude a. Through extrapolations to zero temperature, it finds R_min→0 and Q→0 for a>a_max, suggesting a naked curvature singularity at T=0; at T>0, naked singularities are avoided but the phase structure is rich due to nonuniqueness and hovering black-hole branches. The results illuminate how boundary data, temperature, and conserved charges influence cosmic censorship in holographic AdS setups and point to potential stabilization mechanisms via charged matter.

Abstract

We present a plausible counterexample to cosmic censorship in four dimensional Einstein-Maxwell theory with asymptotically anti-de Sitter boundary conditions. Smooth initial data evolves to a region of arbitrarily large curvature that is visible to distant observers. Our example is based on a holographic model of an electrically charged, localised defect which was previously studied at zero temperature. We partially extend those results to nonzero temperatures.

Figures (9)

• Figure 1: Isometric embeddings of the deformed planar horizon into $\mathbb{R}^3$.
• Figure 2: Isometric embedding of the deformed planar horizon into $\mathbb{R}^3$, coloured with the charge density on the horizon. This solution has $a=30$ and $T=0.119$.
• Figure 3: The minimum radius of the neck region of the horizon as a function of temperature, for amplitude $a = 10$.
• Figure 4: Plots of the total charge as a function of temperature, for two values of the amplitude $a$. For our profile, $a_{\max}\approx8$.
• Figure 5: The square of the Maxwell field, $-F^2(0)$, and the induced scalar curvature of the horizon, $\mathcal{R}(0)$, both evaluated where the horizon meets the axis. The black dots represent black mushrooms at fixed amplitude $a = 10$ and different temperatures. The dashed blue line represents the same quantities for spherical extremal Reissner-Nordström black holes. The two curves approach each other for low temperature black mushrooms.