Testing the cosmic censorship conjecture with point particles: The effect of radiation reaction and the self-force

A classical thought-experiment to destroy black holes was envisaged by Wald in 1974: it consists of throwing particles with large angular momentum into an extremal black hole, checking whether their capture can overspin the black hole past the extremal limit and create a naked singularity. Wald showed that in the test-particle limit, particles that would be otherwise capable of producing naked singularities are simply scattered. Recently, Jacobson and Sotiriou showed that if one considers instead a black hole that is almost, but not exactly extremal, then in the absence of backreaction effects particle capture could indeed overspin the spacetime above the Kerr limit. Here we analyze backreaction effects and 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.

Figure 1

The radial evolution with coordinate time, for geodesics having $E=(E_{\max }+E_{\min })/2=2ϵ$ and $L=b_{\mathrm{ph}}E(1-k)$ with $k=\mu ={10}^{-5}$, in Kerr spacetimes with $a=0.99$, 0.994, 0.998, and 0.9998. In particular, $r$ and $r_H$ are the Boyer-Lindquist coordinates of the particle and of the horizon.

Figure 2

Demonstration of our time-domain Teukolsky code’s convergence rate, for $a=0.9998$ and $m=2$.

Figure 3

Fractional difference between the energy fluxes emitted in a single orbit at the light-ring for $\mu ={10}^{-3}$ and $\mu ={10}^{-5}$ (filled symbols), and for $\mu ={10}^{-7}$ and $\mu ={10}^{-5}$ (empty symbols). The fluxes are obtained by summing over all multipole moments (“total” fluxes, represented by squares) using the prescription outlined in Sec. 3c, or by summing only up to $m=10$ (fluxes “up to $m=10$,” represented by circles).