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 percents from their conformally flat counterparts, whether those solutions share the same dynamical stabilities 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 postmerger-like rotation laws, and perform conformally flat evolutions and analysis over dynamical timescales. We found that the stellar profiles of quasi-toroidal models with high angular momentum for J 9 \;G M_² / c can change significantly over dynamical timescales. In contrast, all the quasi-spherical models considered in this work remain stable even with high angular momentum J=9\;G M_² / c. Our investigation suggest that the quasi-spherical models are suitable initial data for long-lived hypermassive neutron star modelings in conformally flat spacetime.