2D Density Evolution

Density and Ergoregion Evolution

Here we look at the time evolution of the rest-mass density and ergoregion in 2 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. We present two different crosssectional views of the neutron star and ergoregion; an XY (equatorial) crossection and an XZ (meridional) crossection. Select times are chosen to highlight the instability of the ergoregion (green donut). The green dashed line represents $g_{tt} = 0$ while the green region within the dashed lines represents $g_{tt} \gt 0$. The final configuration is a stationary Kerr black hole, as expected.

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XY (equatorial) Crossection

Fig. 1-1: Density and ergoregion at time $t/P_c$ = 0	Fig. 1-2: Density and ergoregion at time $t/P_c$ = 1.02	Fig. 1-3: Density and ergoregion at time $t/P_c$ = 2.05
Fig. 1-4: Density and ergoregion at time $t/P_c$ = 3.02	Fig. 1-5: Density and ergoregion at time $t/P_c$ = 3.99	Fig. 1-6: Density and ergoregion at time $t/P_c$ = 5.01
Fig. 1-7: Density and ergoregion at time $t/P_c$ = 6.41	Fig. 1-8: Density and ergoregion at time $t/P_c$ = 6.52	Fig. 1-9: Black Hole and ergoregion at time $t/P_c$ = 9.00