Abstract
We examine the strong cosmic censorship in the Reissner–Nordstrom–de Sitter (RN-dS) black hole by investigating the evolution of a scalar field non-minimally coupled to the curvature. We find that for the stable RN-dS black hole, with the increase of the coupling parameter, the violation of the strong cosmic censorship occurs at a larger critical charge ratio. But such an increase of the critical charge is suppressed by the increase of the cosmological constant. Different from the minimal coupling situation, it is possible to accommodate beta ge 1 in the near extremal black hole when the scalar field is non-minimally coupled to curvature. beta here is defined as beta equiv -frac{mathrm {Im};omega }{kappa _{-}} where kappa _{-} is the surface gravity of Cauchy horizon and omega is the frequency of quasinormal modes. The increase of the cosmological constant can allow beta ge 1 to be satisfied for even smaller value of the coupling parameter. The existence of beta ge 1 implies that the resulting curvature can continuously cross the Cauchy horizon.
Highlights
When one considers the de Sitter ( > 0) black holes, the situation we discussed above will change dramatically
We have investigated the stability of the Reissner–Nordstrom–de Sitter (RN-dS) black hole and the Strong Cosmic Censorship (SCC) under such a perturbation by applying asymptotic iteration method (AIM) method to calculate out the quasi-normal modes (QNMs)
With the increase of the non-negative coupling parameter, the violation of the SCC occurs at a larger critical charge ratio
Summary
When one considers the de Sitter ( > 0) black holes, the situation we discussed above will change dramatically. The SCC in lukewarm RN-dS and Martnez–Troncoso–Zanelli black hole spacetime under the non-minimally coupled massive scalar perturbation was investigated and it was shown that the validity of the SCC depends on the characteristics of the scalar field [15]. We will not impose any relations between black hole charge Q and mass M, and we will disclose the general validity of the strong cosmic censorship in four-dimensional Reissner–Nordström–de Sitter black hole against non-minimal coupling massless neutral scalar field perturbations. [7], the generic perturbations arising from the smooth initial data can be arbitrarily smooth at the CH when the black holes are close enough to extremality as well as large enough in a dS spacetime This leads to the potential violation of Cr formulation of SCC with any r ≥ 2.
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