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

Abstract

We present the Fermi story of strong cosmic censorship in the near-extremal Reissner-Nordstromde 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 = 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. *

Strong cosmic censorship for a scalar field in a Born-Infeld–de Sitter black hole

“…Recently, the validity of the Christodoulou version of SCC has been explored in asymptotically dS black holes by computing β for various perturbation fields [30][31][32][33][34][35][36][37][38][39][40][41][42][43]. In particular, a massless neutral scalar perturbation field in a Reissner-Nordstrom-de Sitter (RN-dS) black hole was considered in [30], and it was proven that SCC is violated in the near-extremal regime.…”

“…These oscillations were dubbed as "wiggles", which result from non-perturbative effects and can lead to a violation of SCC for an arbitrary large scalar field charge . Later, SCC in a RN-dS black hole was also discussed in the context of the Dirac perturbation field [35,36] and higher space-time dimensions [37,38], where there still exists some room for the violation of SCC. Considering smooth initial data, the violation of SCC becomes more severe for the coupled linearized electromagnetic and gravitational perturbations in a RN-dS black hole [39].…”

Strong cosmic censorship conjecture in higher curvature gravity

“…In the absence of a general proof for strong cosmic censorship conjecture, such an analysis plays a very crucial role in order to test the conjecture, i.e., by looking for possible counterexamples. This approach have been used recently by several authors in order to test the validity of strong cosmic censorship conjecture conjecture for general relativity on various asymptotically de Sitter black hole spacetimes in four and higher dimensions [12][13][14][15][16][17][18][19][20][21][22][23]. The central result arising out of these analyses is the realization that the strong cosmic censorship conjecture is violated in the near extremal regime for non-rotating black holes, while for rotating black holes, the violation can be avoided.…”

Strong cosmic censorship in charged de sitter spacetime with scalar field non-minimally coupled to curvature

“…In order to examine the stability of the Reissner-Nordstrom-de Sitter(RN-dS) black holes, the QNMs have been investigated at various aspects, including the charged scalar field perturbation in four dimension [4], and the gravitational perturbation in higher dimensions [5,6]. In particular, due to the above relation between QNMs and SCC, the QNMs of RN-dS black holes have recently attracted resurgent attentions [1,2,7,8,9,10,11,12,13,14,15,16,17] since the pioneering work [2]. The linear neutral massless scalar perturbation is studied respectively in dimension d = 4 [2], and in higher dimensions [16].…”