Gravitational collapse in anti de Sitter space

A numerical and analytic treatment is presented here of the evolution of initial data of the kind that was conjectured by Hertog, Horowitz and Maeda to lead to a violation of cosmic censorship. That initial data is essentially a thick domain wall connecting two regions of anti de Sitter space. The evolution results in no violation of cosmic censorship, but rather the formation of a small black hole.

Figure 1

the scalar field $\varphi$ at $t=0$. $R=100$ and $N=256000$

Figure 2

the constraint at $t=0.5$ for $R=100$ at two different resolutions: $\mathcal{C}$ for $N=256000$ (solid line) and $8\mathcal{C}$ for $N=512000$ (dashed line)

Figure 3

the scalar field $\varphi$ at $t=0.731$. $R=100$ and $N=256000$

Figure 4

$Y$ at $t=0.731$. $R=100$ and $N=256000$

Figure 5

$r\varphi$ as a function of $t+\rho$ at $t=0.2$ (solid line) and $t=0.4$ (dashed line). $R=100$ and $N=256000$

Figure 6

$\varphi$ as a function of $r$ at $t=0.2$ (solid line) and $t=0.4$ (dashed line). $R=100$ and $N=256000$

Figure 7

$\varphi$ at the final time. $R=100$ and $N=256000$

Figure 8

$Y$ at the final time. $R=100$ and $N=256000$

Figure 9

$a$ at the final time. $R=100$ and $N=256000$

Figure 10

$\varphi$ at $t=0.1$. $R=600$ and $N=1024000$

Figure 11

$Y$ at $t=0.1$. $R=600$ and $N=1024000$

Figure 12

$\varphi$ at $t=0.1$. $R=100$ and $N=256000$

Figure 13

$Y$ at $t=0.1$. $R=100$ and $N=256000$