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

TL;DR

This study examines the stability of hot, differentially rotating hypermassive neutron stars in conformally flat spacetime, revealing stability in quasi-spherical models but potential instability in high angular momentum quasi-toroidal models.

Contribution

It constructs and analyzes hot hypermassive neutron star models with high angular momentum in conformally flat spacetime, highlighting stability differences based on geometry.

Findings

Quasi-spherical models remain stable at high angular momentum.

High angular momentum quasi-toroidal models may become unstable.

Conformally flat models are suitable for initial data in long-term neutron star simulations.

Abstract

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 percent 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 post-merger-like rotation laws, and perform conformally flat evolutions and analysis over dynamical timescales. We find that enforcing conformally-flat spacetime could change the equilibrium of quasi-toroidal models with high angular momentum for $J \gtrsim 9 ~G M_{\odot}^2 / c$ compared to fully general relativistic cases. In contrast, all the quasi-spherical models considered in this work remain stable even with high angular momentum $J=9~G M_{\odot}^2 / c$. Our investigation suggests that the quasi-spherical models are suitable initial data for long-lived hypermassive neutron star modeling in conformally flat spacetime.