Dynamical stability of quasitoroidal differentially rotating neutron stars

We investigate the dynamical stability of relativistic, differentially rotating, quasitoroidal models of neutron stars through hydrodynamical simulations in full general relativity. We find that all quasitoroidal configurations studied in this work are dynamically unstable against the growth of nonaxisymmetric 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 quasitoroidal 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/M2>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.