Collapse of differentially rotating neutron stars and cosmic censorship

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 the one 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.

💡 Research Summary

The paper investigates the dynamical stability and gravitational‑wave (GW) emission of differentially rotating neutron stars (NSs) using a relativistic polytropic equation of state (EOS) and the “j‑constant” law for differential rotation. The authors construct equilibrium models with a range of the dimensionless spin parameter χ = J/M², separating them into sub‑Kerr (χ < 1) and supra‑Kerr (χ > 1) families. For sub‑Kerr models they identify configurations that are dynamically unstable: these collapse promptly to rotating (Kerr) black holes (BHs). The collapse proceeds almost axisymmetrically; non‑axisymmetric modes have insufficient time to grow, and the GW signal resembles that of uniformly rotating collapse but with a modestly lower efficiency (∼10⁻⁶ of the rest‑mass energy).

In contrast, all supra‑Kerr models studied are dynamically stable. To force a collapse the authors artificially reduce the pressure support by up to 99 %. The resulting evolution forms a massive torus that quickly develops strong non‑axisymmetric instabilities (bar‑mode and corotation‑type modes). Rather than forming a BH, the torus redistributes angular momentum and settles into a new axisymmetric equilibrium configuration. No event horizon appears, and the final object remains a massive, differentially rotating NS. Consequently, the simulations do not produce naked singularities, supporting the cosmic censorship conjecture even for χ > 1 progenitors.

The GW emission from the forced supra‑Kerr collapse is markedly different: the torus’ non‑axisymmetric dynamics generate higher‑amplitude, broader‑band signals than the sub‑Kerr cases, suggesting that future GW detectors could, in principle, distinguish between these two collapse pathways.

Overall, the study demonstrates that differential rotation can raise the maximum allowed J/M² above the Kerr limit for equilibrium NSs, but natural dynamical instabilities do not drive such supra‑Kerr stars to BH formation. Only extreme, non‑physical reductions of pressure trigger collapse, and even then the system avoids forming a naked singularity. These results reinforce the robustness of cosmic censorship and provide valuable predictions for GW signatures of differentially rotating NS collapse.