Strong cosmic censorship in de Sitter space

Abstract

Recent work indicates that the strong cosmic censorship hypothesis is violated by nearly extremal Reissner-Nordström-de Sitter black holes. It was argued that perturbations of such a black hole decay sufficiently rapidly that the perturbed spacetime can be extended across the Cauchy horizon as a weak solution of the equations of motion. In this paper we consider the case of Kerr-de Sitter black holes. We find that, for any non-extremal value of the black hole parameters, there are quasinormal modes which decay sufficiently slowly to ensure that strong cosmic censorship is respected. Our analysis covers both scalar field and linearized gravitational perturbations.

The BTZ black hole violates strong cosmic censorship

“…This ensures that, when backreaction is included, the Einstein equation cannot be satisfied, even in the sense of weak solutions, at CH + R (see e.g. [15]). From (3.46), the condition for this is β < 1/2, as in [11,15].…”

“…In particular, it has been shown that linearized gravitational and electromagnetic perturbations of such a hole can be arbitrarily differentiable at the Cauchy horizon if the black hole is near-extremal and large enough [12]. On the other hand, it has been shown that linear gravitational perturbations of a Kerr-de Sitter black hole exhibit behaviour that is in agreement with strong cosmic censorship [15].…”

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.…”

“…In [40], the authors proved that nonlinear effects could not save SCC from being violated for a near-extremal RN-dS black hole. On the other hand, SCC is always respected for the massless scalar field and linearized gravitational perturbations in a Kerr-dS black hole [37,41].…”

On the viability of regular black holes

“…While still being an active research area (see, for instance, the recent works [28][29][30][31] 1 ), the main aspects were settled more than two decades ago [32][33][34][35][36][37], though formal proofs of a number of technical aspects were only available later [38] (see also [39] for a review). In brief terms, the central conclusion of these works is that the inner horizon is unstable in the presence of both ingoing and outgoing perturbations, which are expected to exist in realistic collapse scenarios.…”