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

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 con- formal 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 indepen- dent 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.