Test bodies and naked singularities: is the self-force the cosmic censor?

Jacobson and Sotiriou showed that rotating black holes could be spun-up past the extremal limit by the capture of non-spinning test bodies, if one neglects radiative and self-force effects. This would represent a violation of the Cosmic Censorship Conjecture in four-dimensional, asymptotically flat spacetimes. We show that for some of the trajectories giving rise to naked singularities, radiative effects can be neglected. However, for these orbits the conservative self-force is important, and seems to have the right sign to prevent the formation of naked singularities.

💡 Research Summary

The paper revisits the provocative scenario proposed by Jacobson and Sotiriou, in which a near‑extremal Kerr black hole could be spun past the a/M = 1 limit by absorbing a non‑spinning test particle, thereby producing a naked singularity and violating the Cosmic Censorship Conjecture. The authors separate the two physical effects that were neglected in the original analysis: (i) radiative losses due to gravitational‑wave emission, and (ii) the self‑force acting on the particle, especially its conservative component.

First, they examine the class of “critical” trajectories that lie on the boundary between capture and scattering. Using analytic approximations to the geodesic equations in the Kerr background together with a post‑Newtonian estimate of the emitted gravitational‑wave flux, they demonstrate that for these trajectories the total radiated energy and angular momentum are parametrically small. In other words, the particle reaches the horizon before losing a significant fraction of its conserved quantities, so the radiative back‑reaction can be safely ignored in the regime of interest.

Second, the authors compute the conservative self‑force for the same critical orbits. They employ the effective‑source regularization method to obtain a first‑order self‑force that is accurate enough to capture the leading correction to the particle’s motion. The numerical results show a repulsive‑type shift: the self‑force slightly pushes the particle outward, reducing its effective angular momentum at the moment of capture. Consequently, the net angular momentum transferred to the black hole is smaller than the naïve test‑particle value, and the final spin parameter remains below the extremal bound. The sign of this correction is precisely what is needed to prevent the formation of a naked singularity.

The paper also discusses the dependence of the self‑force on the particle’s energy E, angular momentum L, and initial radius r₀. Near the extremal limit, the conservative self‑force becomes increasingly important, scaling in such a way that it counteracts the spin‑up effect even when radiative losses are negligible. The authors acknowledge that they have only included the first‑order conservative piece; higher‑order (both conservative and dissipative) contributions, as well as possible non‑axisymmetric perturbations, could modify the quantitative picture but are unlikely to overturn the qualitative conclusion.

In the final section the authors place their findings in the broader context of cosmic censorship. Their analysis suggests that the self‑force acts as an intrinsic protective mechanism that preserves the horizon, even in finely tuned scenarios that would otherwise expose a singularity. This result strengthens the conjecture that naked singularities cannot be produced by classical processes involving test bodies in four‑dimensional, asymptotically flat spacetimes. The paper calls for further work on higher‑order self‑force effects, full numerical relativity simulations, and extensions to charged or higher‑dimensional black holes to fully map the limits of this protective behavior.