It was recently shown that Strong Cosmic Censorship might be violated for near-extremally-charged black holes in 4-dimensional de Sitter space under scalar perturbations. Here, we extend the study of neutral massless scalar perturbations in higher dimensions and discuss the dimensional influence on the validity of Strong Cosmic Censorship hypothesis. By giving an elaborate description of neutral massless scalar perturbations of Reissner-Nordström-de Sitter black holes in d = 4, 5 and 6 dimensions we conclude that Strong Cosmic Censorship is violated near extremality.

Most available studies of quasi-normal modes for Lifshitz black solutions are limited to the neutral scalar perturbations. In this letter, we investigate the wave dynamics of massive charged scalar perturbation in the background of (3 + 1)-dimensional charged dilaton Lifshitz black branes/holes. We disclose the dependence of the quasi-normal modes on the model parameters, such as the Lifshitz exponent z, the mass and charge of the scalar perturbation field and the charge of the Lifshitz configuration. In contrast with neutral perturbations, we observe the possibility to destroy the original Lifshitz background near the extreme value of charge where the temperature is low. We find out that when the Lifshitz exponent deviates more from unity, it is more difficult to break the stability of the configuration. We also study the behavior of the real part of the quasi-normal frequencies.Unlike the neutral scalar perturbation around uncharged black branes where an overdamping was observed to start at z = 2 and independent of the value of scalar mass, our observation discloses that the overdamping starting point is no longer at z = 2 and depends on the mass of scalar field for charged Lifshitz black branes. For charged scalar perturbations, fixing ms, the asymptotic value of ωR for high z is more away from zero when the charge of scalar perturbation qs increases. There does not appear the overdamping. * Electronic address: mkzangeneh@shirazu.ac.ir † Electronic address: wang b@sjtu.edu.cn ‡ Electronic address: asheykhi@shirazu.ac.ir § Electronic address: tangziyu@sjtu.edu.cn

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We investigate the spacetime properties of BTZ black holes in the presence of the Maxwell field and BornInfeld field and find rich properties in the spacetime structures when the model parameters are varied. Employing LandauLifshitz theory, we examine the thermodynamical phase transition in the charged BTZ black holes. We further study the dynamical perturbation in the background of the charged BTZ black holes and find different properties in the dynamics when the thermodynamical phase transition occurs.

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A large class of spherically symmetric static extremal black hole spacetimes possesses a stable null photon sphere on their horizons. For the extremal Kerr-Newman family, the photon sphere only really coincides with the horizon in the sense clarified by Doran. The condition under which photon orbit is stable on an asymptotically flat extremal Kerr-Newman black hole horizon has recently been clarified; it is found that a sufficiently large angular momentum destabilizes the photon orbit, whereas electrical charge tends to stabilize it. We investigated the effect of a negative cosmological constant on this observation, and found the same behavior in the case of an extremal asymptotically Kerr-Newman-AdS black holes in (3 + 1)-dimensions. In (2 + 1)-dimensions, in the presence of electrical charge, the angular momentum never becomes large enough to destabilize the photon orbit. We comment on the instabilities of black hole spacetimes with a stable photon orbit.

We consider Maxwell-f (R) gravity and obtain an exact charged black hole solution with dynamic curvature in D-dimensions. Considering a spherically symmetric metric ansatz and without specifying the form of f (R) we find a general black hole solution in D-dimensions.This general black hole solution can be reduced to the Reissner-Nordström (RN) black hole in D-dimensions in Einstein gravity and to the known charged black hole solutions with constant curvature in f (R) gravity. Restricting the parameters of the general solution we get polynomial solutions which reveal novel properties when compared to RN black holes.Specifically we study the solution in (3 + 1)-dimensions in which the form of f (R) can be solved explicitly giving a dynamic curvature and compare it with the RN black hole. We also carry out a detailed study of its thermodynamics.

We discuss black hole solutions in (2+1)-dimensions with a scalar field non-minimally coupled to Einstein's gravity in the presence of a cosmological constant and a self-interacting scalar potential. Without specifying the form of the potential, we find a general solution of the field equations, which includes all the known asymptotically anti-de Sitter (AdS) black hole solutions in (2+1)-dimensions as special cases once values of the coupling constants are chosen appropriately. In addition, we obtain numerically new black hole solutions and for some specific choices of the coupling constants we derive new exact AdS black hole solutions.We also discuss the possibility of obtaining asymptotically de Sitter black hole solutions with or without an electromagnetic field.