# On the dynamical stability of quasi-toroidal differentially rotating neutron stars

## TL;DR

This study uses full general relativity simulations to analyze the stability of quasi-toroidal, differentially rotating neutron stars, revealing that such configurations are generally unstable and that exceeding the Kerr bound does not guarantee stability.

## Contribution

It provides the first comprehensive dynamical stability analysis of relativistic, quasi-toroidal neutron star models, challenging assumptions about their longevity and stability.

## Key findings

- All studied quasi-toroidal models are dynamically unstable.
- High rest mass configurations collapse into black holes.
- Supra-Kerr models can undergo catastrophic collapse without violating cosmic censorship.

## Abstract

We investigate the dynamical stability of relativistic, differentially rotating, quasi-toroidal models of neutron stars through hydrodynamical simulations in full general relativity. We find that all quasi-toroidal configurations studied in this work are dynamically unstable against the growth of non-axisymmetric modes. Both one-arm and bar mode instabilities grow during their evolution. We find that very high rest mass configurations collapse to form black holes. Our calculations suggest that configurations whose rest mass is less than the binary neutron star threshold mass for prompt collapse to black hole transition dynamically to spheroidal, differentially rotating stars that are dynamically stable, but secularly unstable. Our study shows that the existence of extreme quasi-toroidal neutron star equilibrium solutions does not imply that long-lived binary neutron star merger remnants can be much more massive than previously found. Finally, we find models that are initially supra-Kerr ($J/M^2>1$) and undergo catastrophic collapse on a dynamical timescale, in contrast to what was found in earlier works. However, cosmic censorship is respected in all of our cases. Our work explicitly demonstrates that exceeding the Kerr bound in rotating neutron star models does not imply dynamical stability.