Strong cosmic censorship for the massless Dirac field in the Reissner-Nordstrom-de Sitter spacetime

TL;DR

This paper investigates the stability of the strong cosmic censorship conjecture for massless Dirac fields in near-extremal Reissner-Nordstrom-de Sitter black holes, deriving conditions for violation and showing recovery of censorship under certain charge conditions.

Contribution

It derives the quasi-normal mode criterion for Dirac fields in this spacetime and demonstrates how the censorship can be restored by increasing the Dirac field's charge.

Findings

Quasi-normal mode criterion for Dirac fields matches that for Bose fields.

Strong cosmic censorship can be recovered for certain charge thresholds.

The critical charge increases as the black hole approaches extremality.

Abstract

We present the Fermi story of strong cosmic censorship in the near-extremal Reissner-Nordstrom-de Sitter black hole. To this end, we first derive from scratch the criterion for the quasi-normal modes of Dirac field to violate strong cosmic censorship in such a background, which turns out to be exactly the same as those for Bose fields, although the involved energy momentum tensor is qualitatively different from that for Bose fields. Then to extract the low-lying quasi-normal modes by Prony method, we apply Crank-Nicolson method to evolve our Dirac field in the double null coordinates. As a result, it shows that for a fixed near-extremal black hole, strong cosmic censorship can be recovered by the $l=\frac{1}{2}$ black hole family mode once the charge of our Dirac field is greater than some critical value, which is increased as one approaches the extremal black hole.