Strong cosmic censorship for the Dirac field in the higher dimensional Reissner-Nordstrom--de Sitter black hole

TL;DR

This paper studies the violation and restoration of strong cosmic censorship in higher-dimensional Reissner-Nordstrom--de Sitter black holes under Dirac field perturbations, using numerical and analytical methods across different spacetime dimensions.

Contribution

It derives a dimension-independent criterion for cosmic censorship violation and demonstrates how increasing Dirac field charge restores censorship near extremality.

Findings

Violations occur in near-extremal black holes for neutral Dirac fields.

Increasing the Dirac field charge beyond a critical value restores cosmic censorship.

The critical charge depends on how close the black hole is to extremality.

Abstract

We investigate the strong cosmic censorship for the Dirac field in the higher dimensional Reissner-Norstrom--de Sitter black hole. To achieve this, we first use the conformal transformation trick to massage the Dirac equation to a pair of coupled equations in a meticulously chosen orthonormal basis and derive the criterion on the quasinormal modes for the violation of the strong cosmic censorship, which turns out to be independent of the spacetime dimension. Then we apply the Crank-Nicolson method to evolve our Dirac equation in the double null coordinates and extract the low-lying quasinormal modes from the evolution data by the Prony method. It is shown for the spacetime dimension $D=4, 5, 6$ under consideration that although the strong cosmic censorship is violated by the perturbation from the neutral Dirac field in the near-extremal black hole, the strong cosmic censorship can be restored when the charge of the Dirac field is increased beyond a critical value. The closer to the extremal limit the black hole is, the larger the critical charge of the Dirac field is.