In this paper, we study a physical system that is composed of massive charged scalar field linearly coupled to a charged rotating Kerr-Newman black hole. Given the parameters of black hole and a specific set of "quantum" numbers, the parameter space of the scalar field, which is a plane spanned by its mass and charge, is divided into five partitions by three simple constraint lines and the existence line of scalar clouds. The physical properties of the system in these partitions are presented. It is found that superradiant instability may be possibly caused only in two of the partitions. In particular, it is shown that both the mass and charge of the scalar clouds are bounded in a limited region. Our results may be used to rapidly judge the possible occurrence of superradiant instability and the existence of scalar clouds around a given black hole.

We study the scalar perturbation on the background of a Kerr black hole in the dynamical Chern-Simons modified gravity with a quadratic coupling between the scalar field and Chern-Simons term. In particular, the late-time tails of scalar perturbations are investigated numerically in time domain by using the hyperboloidal foliation method. It is found that the Kerr black hole becomes unstable under linear perturbations in a certain region of the parameter space, which depends on the harmonic azimuthal index m of the perturbation's mode. This may indicate that some Kerr black holes in this theory will get spontaneously scalarized into a non-Kerr black hole. *

We study the photon's motion around a black hole in the presence of a plasma whose density is a function of the radius coordinate by a renewed ray-tracing algorithm and investigate the influence of the plasma on the shadow of the black hole. The presence of plasma affects not only the size but also the shape of black hole shadow. Furthermore, the influence of plasma on trajectories of photons depends on the frequency of photon. For the high-frequency photons, the influence is negligible, on the contrary, the trajectories of low-frequency photons is affected significantly by the plasma. Interestingly, it is also found that the black hole image would take on a multi-ring structure due to the presence of plasma.

We have studied the shadow of a regular phantom black hole as photons couple to the Weyl tensor. We find that due to the coupling photons with different polarization directions propagate along different paths in the spacetime so that there exists a double shadow for a black hole, which is quite different from that in the non-coupling case where only a single shadow emerges. The overlap region of the double shadow, the umbra, of the black hole increases with the phantom charge and decreases with the coupling strength. The dependence of the penumbra on the phantom charge and the coupling strength is converse to that of the umbra. Combining with the supermassive central object in our Galaxy, we estimated the shadow of the black hole as the photons couple to the Weyl tensor. Our results show that the coupling brings about richer behaviors of the propagation of coupled photon and the shadow of the black hole in the regular phantom black hole spacetime.

In this paper, the behaviour of a charged massive scalar test field in the background of a Kerr–Sen black hole is investigated. A type of stationary solutions, dubbed scalar clouds, are obtained numerically and expressed by the existence lines in the parameter space. We show that for fixed background and a given set of harmonic indices, the mass and charge of the scalar clouds are limited in a finite region in the parameter space of the scalar field. Particularly, the maximum values of the mass and charge of the clouds around extremal Kerr–Sen black holes are independent of the angular velocity of the black hole, whereas those in the extremal Kerr–Newman background depend on the angular velocity. In addition, it is demonstrated that, as the static limit of the Kerr–Sen black hole, the Gibbons–Maeda–Garfinkle–Horowitz–Strominger black hole cannot support scalar cloud.