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 stable oscillatory behavior. Later in the evolution the star relaxes to stationary equilibrium. The star remains dynamically stable for 30 rotation periods or 100 dynamical timescalses. This specific ergostar is the first member that exhibits an ergoregion along a constant rest-mass (central) denstiy $\rho_0 = 4.52\times 10^{14} \mathrm{g/cm^3}$ sequence with a decreasing $R_p/R_e$ ratio and the j-const law with $\hat{A} = 5$. Here 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 stability of the ergoregion (green donut). The green dashed line represents $g_{tt} = 0$ while the green region within the dashed lines represents $g_{tt} \gt 0$.

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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 $t/P_c$ = 1.04	Fig. 1-3: Density and ergoregion at time $t/P_c$ = 3.03
Fig. 1-4: Density and ergoregion at time $t/P_c$ = 4.02	Fig. 1-5: Density and ergoregion at time $t/P_c$ = 4.52	Fig. 1-6: Density and ergoregion at time $t/P_c$ = 5.01
Fig. 1-7: Density and ergoregion at time $t/P_c$ = 9.98	Fig. 1-8: Density and ergoregion at time $t/P_c$ = 14.99	Fig. 1-9: Density and ergoregion at time $t/P_c$ = 20.00

Fig. 1-10: Density and ergoregion at time $t/P_c$ = 25.02

Fig. 1-11: Density and ergoregion at time $t/P_c$ = 30.03