High angular momentum hot differentially rotating equilibrium star evolutions in conformally flat spacetime

The conformal flatness approximation to the Einstein equations has been successfully used in many astrophysical applications such as initial data constructions and dynamical simulations. Although it has been shown that full general relativistic strongly differentially rotating equilibrium models deviate by at most a few percentage from their conformally flat counterparts, whether those conformally flat solutions remain stable has not been fully addressed. To further understand the limitations of the conformal flatness approximation, in this work, we construct spatially conformally flat hot hypermassive neutron stars with postmergerlike rotation laws, and perform conformally flat evolutions and analysis over dynamical timescales. We find that enforcing conformally flat spacetime could change the equilibrium of quasitoroidal models with high angular momentum for 𝐽≳9  𝐺⁢𝑀2⊙/𝑐 compared to fully general relativistic cases. In contrast, all the quasispherical models considered in this work remain stable even with high angular momentum 𝐽=9  𝐺⁢𝑀2⊙/𝑐. Our investigation suggests that the quasispherical models are suitable initial data for long-lived hypermassive neutron star modeling in conformally flat spacetime.