We present new results on the dynamics and gravitational-wave emission from the collapse of differentially rotating neutron stars. We have considered a number of polytropic stellar models having different values of the dimensionless angular momentum $J/M^2$, where $J$ and $M$ are the asymptotic angular momentum and mass of the star, respectively. For neutron stars with $J/M^2<1$, i.e. “sub-Kerr” models, we were able to find models that are dynamically unstable and that collapse promptly to a rotating black hole. Both the dynamics of the collapse and the consequent emission of gravitational waves resemble those seen for uniformly rotating stars, although with an overall decrease in the efficiency of gravitational-wave emission. For stellar models with $J/M^2>1$, i.e. “supra-Kerr” models, on the other hand, we were not able to find models that are dynamically unstable and all of the computed supra-Kerr models were found to be far from the stability threshold. For these models a gravitational collapse is possible only after a very severe and artificial reduction of the pressure, which then leads to a torus developing nonaxisymmetric instabilities and eventually contracting to a stable axisymmetric stellar configuration. While this does not exclude the possibility that a naked singularity can be produced by the collapse of a differentially rotating star, it also suggests that cosmic censorship is not violated and that generic conditions for a supra-Kerr progenitor do not lead to a naked singularity.

• Received 3 May 2011

DOI:https://doi.org/10.1103/PhysRevD.84.024022