Spin-2 fields and cosmic censorship

Abstract

We evaluate the possibility of the formation of naked singularities in the interaction of Kerr black holes with test massless spin-2 fields. We analyse the scattering problem for both extremal and nearly extremal black holes by incorporating the explicit form of the absorption probabilities. We show that extremal black holes become non-extremal after the interaction with the modes with both positive and negative absorption probabilities. For nearly extremal black holes the absorption probability for the challenging modes turns out to be of the order ${\epsilon }^5$, where $\epsilon$ parametrizes the closeness to extremality. Though the highest absorption probability for $m=2$ modes pertains to spin-2 fields, its drastically small value implies that the event horizon is preserved without the need to employ the backreaction effects. The result can be qualitatively extrapolated to hypothetical higher integer spin fields. We also review and extend our previous comments on Sorce-Wald method. We show that the order magnitude problems can be avoided by abandoning the non-physical parameter $\lambda$. The conditions derived by Sorce-Wald can be legitimately used to incorporate the back-reaction effects by avoiding to multiply them by ${\lambda }^2$, thereby preserving the magnitude of their contribution. We apply this method to the problems of over-charging R-N black holes and over-spinning Kerr black holes, in a rough analysis ignoring absorption probabilities which could apply to test bodies.

Includes appendix (second order Sorce-Wald condition for Kerr and R-N black holes)

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