Numerical Simulations of Generic Singularities

Numerical simulations of the approach to the singularity in vacuum spacetimes are presented here. The spacetimes examined have no symmetries and can be regarded as representing the general behavior of singularities. It is found that the singularity is spacelike and that, as it is approached, the spacetime dynamics becomes local and oscillatory.

Figure 1

Maximum values of $\ln |E_{\alpha }{}^i|$ (solid line), $\ln |r_{\alpha }|$ (dotted line) and $\ln |A^{\alpha }|$ (dot-dashed line) vs time.

Figure 2

Constraint ${\mathcal{C}}_q$ vs time, for $n=50$ (solid line) and $n=25$ (dot-dashed line).

Figure 3

Components of ${\Sigma }_{\alpha \beta }$ vs time, in the asymptotic frame: ${\Sigma }_1$ (solid line), ${\Sigma }_2$ (dotted line) and ${\Sigma }_3$ (dot-dashed line).

Figure 4

Components of $N_{\alpha \beta }$ vs time, in the asymptotic frame: $N_1$ (solid line), $N_2$ (dotted line) and $N_3$ (dot-dashed line).

Figure 5

$u$ vs time.