3D Density Evolution
Here we look at the time evolution of the rest-mass density and ergoregion in 3 spatial dimensions. The rest-mass density is normalized to its initial maximum value. As the hypermassive neutron star evolves, the ergoregion exhibits oscillatory behavior. Eventually, after a few oscillations, the star becomes unstable and collapses into a black hole with the ergoregion of the star morphing into the ergoregion of a stationary black hole. The criterion that $\mathbf{t} \cdot \mathbf{t} = g_{tt} = 0$ marks the boundary of the ergoregion does not stricly hold in the nonstationary spacetime of a collapsing star; however, it is still a reasonable measure for the boundary given the stationary inital and final gravitational configurations. Select times are chosen to highlight the instability of the ergoregion (green donut). The final configuration is a stationary Kerr black hole, as expected.
 Fig. 1-1: Density and ergoregion at time $t/P_c$ = 0 |
 Fig. 1-2: Density and ergoregion at time $t/P_c$ = 2.01 |
 Fig. 1-3: Density and ergoregion at time $t/P_c$ = 3.09 |
 Fig. 1-4: Density and ergoregion at time $t/P_c$ = 4.01 |
 Fig. 1-5: Density and ergoregion at time $t/P_c$ = 4.47 |
 Fig. 1-6: Density and ergoregion at time $t/P_c$ = 5.09 |
 Fig. 1-7: Black Hole and ergoregion at time $t/P_c$ = 5.86 |
