Cosmic censorship, massless fermionic test fields, and absorption probabilities

TL;DR

This paper re-examines the interaction of massless fermionic fields with black holes, showing that absorption probabilities prevent divergence issues and that overspinning is non-generic, potentially fixed by quantum effects.

Contribution

It introduces a refined approach considering absorption probabilities, demonstrating that divergence problems are resolved and overspinning is non-generic for certain field amplitudes.

Findings

Absorption probabilities eliminate divergence issues in fermionic test fields.

Overspinning of black holes by fermionic fields is non-generic for small amplitudes.

Backreaction effects can prevent overspinning for larger field amplitudes.

Abstract

In the conventional approach, fermionic test fields lead to a generic overspinning of black holes resulting in the formation of naked singularities. The absorption of the fermionic test fields with arbitrarily low frequencies is allowed for which the contribution to the angular momentum parameter of the space-time diverges. Recently we have suggested a more subtle treatment of the problem considering the fact that only the fraction of the test fields that is absorbed by the black hole contributes to the space-time parameters. Here, we re-consider the interaction of massless spin $(1/2)$ fields with Kerr and Kerr-Newman black holes, adapting this new approach. We show that the drastic divergence problem disappears when one incorporates the absorption probabilities. Still, there exists a range of parameters for the test fields that can lead to overspinning. We employ backreaction effects due to the self-energy of the test fields which fixes the overspinning problem for fields with relatively large amplitudes, and renders it non-generic for smaller amplitudes. This non-generic overspinning appears likely to be fixed by alternative semi-classical and quantum effects.