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A classical thought-experiment to destroy black holes was envisaged by Waldin 1974: it consists of throwing particles with large angular momentum into anextremal black hole, checking whether their capture can over-spin the blackhole past the extremal limit and create a naked singularity. Wald showed thatin the test-particle limit, particles that would be otherwise capable ofproducing naked singularities are simply scattered. Recently Jacobson andSotiriou showed that if one considers instead a black hole that is almost, butnot exactly extremal, then in the absence of backreaction effects particlecapture could indeed over-spin the spacetime above the Kerr limit. Here weanalyze back-reaction effects and show that for some of the trajectories givingrise to naked singularities, radiative effects can be neglected. However, forthese orbits the conservative self-force is important, and seems to have theright sign to prevent the formation of naked singularities.

Testing the Cosmic Censorship Conjecture with point particles: the effect of radiation reaction and the self-force