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Register a new userStrong cosmic censorship for charged de Sitter black holes with a charged scalar field
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It has been shown recently that the strong cosmic censorship conjecture is violated by near-extremal Reissner-Nordstrom-de Sitter black holes. We investigate whether the introduction of a charged scalar field can rescue strong cosmic censorship. We find that such a field improves the situation but there is always a neighbourhood of extremality in which strong cosmic censorship is violated by perturbations arising from smooth initial data.
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We discuss charged and static solutions in a shift-symmetric scalar-tensor gravity model including a negative cosmological constant. The solutions are only approximately Anti-de Sitter (AdS) asymptotically. While spherically symmetric black holes with scalar-tensor hair do exist in our model, the uncharged spherically symmetric scalar-tensor solitons constructed recently cannot be generalised to include charge. We point out that this is due to the divergence of the electric monopole at the origin of the coordinate system, while higher order multipoles are well-behaved. We also demonstrate that black holes with scalar hair exist only for horizon value larger than that of the corresponding {it extremal} Reissner-Nordstrom-AdS (RNAdS) solution, i.e. that we cannot construct solutions with arbitrarily small horizon radius. We demonstrate that for fixed $Q$ a horizon radius exists at which the specific heat $C_Q$ diverges - signalling a transition from thermodynamically unstable to stable black holes. In contrast to the RNAdS case, however, we have only been able to construct a stable phase of large horizon black holes, while a stable phase of small horizon black holes does not (seem to) exist.
Recent work indicates that the strong cosmic censorship hypothesis is violated by nearly extremal Reissner-Nordstrom-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.
It has been shown that the Christodoulou version of the Strong Cosmic Censorship (SCC) conjecture can be violated for a scalar field in a near-extremal Reissner-Nordstrom-de Sitter black hole. In this paper, we investigate the effects of higher derivative corrections to the Einstein-Hilbert action on the validity of SCC, by considering a neutral massless scalar perturbation in 5- and 6-dimensional Einstein-Maxwell-Gauss-Bonnet-de Sitter black holes. Our numerical results exhibit that the higher derivative term plays a different role in the d = 5 case than it does in the d = 6 case. For d = 5, the SCC violation region increases as the strength of the higher derivative term increases. For d = 6, the SCC violation region first increases and then decreases as the higher derivative correction becomes stronger, and SCC can always be restored for a black hole with a fixed charge ratio when the higher derivative correction is strong enough. Finally, we find that the C2 version of SCC is respected in the d = 6 case, but can be violated in some near-extremal regime in the d = 5 case.
We study the instability of the charged Gauss-Bonnet de Sitter black holes under gravito-electromagnetic perturbations. We adopt two criteria to search for an instability of the scalar type perturbations, including the local instability criterion based on the $AdS_2$ Breitenl{o}hner-Freedman (BF) bound at extremality and the dynamical instability via quasinormal modes by full numerical analysis. We uncover the gravitational instability in five spacetime dimensions and above, and construct the complete parameter space in terms of the ratio of event and cosmological horizons and the Gauss-Bonnet coupling. We show that the BF bound violation is a sufficient but not necessary condition for the presence of dynamical instability. While the physical origin of the instability without the Gauss-Bonnet term has been argued to be from the $AdS_2$ BF bound violation, our analysis suggests that the BF bound violation can not account for all physical origin of the instability for the charged Gauss-Bonnet black holes.
We study standard Einstein-Maxwell theory minimally coupled to a complex valued and self-interacting scalar field. We demonstrate that new, previously unnoticed spherically symmetric, charged black hole solutions with scalar hair exist in this model for sufficiently large gravitational coupling and sufficiently small electromagnetic coupling. The novel scalar hair has the form of a spatially oscillating wave packet and back-reacts on the space-time such that both the Ricci and the Kretschmann scalar, respectively, possess qualitatively similar oscillations.
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