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 investigate the strong gravitational lensing of spherically symmetric black holes in the novel Einstein–Gauss–Bonnet (EGB) gravity surrounded by unmagnetized plasma medium. The deflection angle in the strong deflection limit in EGB spacetime with homogeneous plasma is derived. We find that both the coupling constant [Formula: see text] in the novel EGB gravity and the presence of plasma can affect the radius of photon sphere, strong field limit coefficient and other lensing observables significantly, while plasma has little effect on the angular image separation and the relative magnifications as [Formula: see text] and [Formula: see text], respectively.

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We investigate the strong deflection gravitational lensing by an Einstein–Lovelock ultracompact object. Its unique features are the relativistic images inside its photon sphere which are absent for an Einstein–Lovelock black hole. We obtain its lensing observables and evaluate their observability for the direct images of two supermassive black holes in the Galaxy and M87 respectively, Sgr A* and M87*, and for the relativistic microlensing on a star closely around Sgr A*. We find that although it is impossible to tell difference of the ultracompact object from the black hole in Einstein–Lovelock gravity by the direct images, it might be possible to distinguish the Einstein–Lovelock ultracompact object by measuring the total flux of the relativistic microlensing in the not-so-far future.

It is recently shown that, besides the Schwarzshcild black hole solution, there exist also scalarized black hole solutions in some Einstein-scalar-Gauss-Bonnet theories. In this paper, we construct analytical expressions for the metric functions and scalar field configurations for these scalarized black hole solutions approximately by employing the continued fraction parametrization method and investigate their thermodynamic stability. It is found that the horizon entropy of a scalarized black hole is always smaller than that of a Schwarzschild black hole, which indicates that these scalarized black holes may decay to Schwarzschild black holes by emission of scalar waves. This fact also implies the possibility to extract the energy of scalar charges.