Violating the Weak Cosmic Censorship Conjecture in Four-Dimensional Anti–de Sitter Space

We consider time-dependent solutions of the Einstein-Maxwell equations using anti–de Sitter (AdS) boundary conditions, and provide the first counterexample to the weak cosmic censorship conjecture in four spacetime dimensions. Our counterexample is entirely formulated in the Poincaré patch of AdS. We claim that our results have important consequences for quantum gravity, most notably to the weak gravity conjecture.

Figure 1

$|F^2|$ at $\xi =0$, $\eta =1$ as a function of $v$ for five different values of $a_0$. For the subcritical amplitudes, the value of $|F^2|$ on the horizon in the corresponding stationary solution can be deduced analytically [12] and is shown as a dotted line.

Figure 2

$v[d(F^2)/dv]$ at $\xi =0$, $\eta =1$ as a function of $v$ for five different values of $a_0$. The symbols and colours are the same as in Fig. 1.

Figure 3

$(v/F^2)d(F^2)/dv$ at $\xi =0$, $\eta =1$ as a function of $v$ for three different values of $a_0$.

Figure 4

Coordinate velocity of an outgoing null geodesic along $\eta =1$ for the $a_0=0.7071$ solution at various times. The inset plot depicts small $\xi$.

Figure 5

Coordinate velocity of an outgoing null geodesic along $\eta =1$ at $\xi =0$ for the $a_0=0.7071$ solution as a function of $v$. The inset plot depicts late $v$.