Circular photon orbits and black hole shadows are significantly important issues in physics and astronomy, and a number of breakthroughs have been witnessed in recent years. Conventionally, the stable and unstable circular photon orbits are obtained using the effective potential of test particles moving in black hole spacetime. In this work, a pure geometric approach is developed to calculate these circular photon orbits and black hole shadow radius. Furthermore, it can be proved that our geometric approach is completely equivalent to the conventional approach based on effective potentials of test particles.

In a recent work Qiao and Li [Phys. Rev. D 106, L021501 (2022)], a new geometric approach is proposed to obtain the photon sphere (circular photon orbit) and the black hole shadow radius. In this approach, photon spheres and the black hole shadow radius are determined using geodesic curvature and Gaussian curvature in the optical geometry of black hole spacetimes. However, the calculations in Qiao and Li only restricted to a subclass of static and spherically symmetric black holes with spacetime metric $g_{tt}·g_{rr}=-1$, $g_{\theta \theta }=r^2$ and $g_{\varphi \varphi }=r^2{\sin }^2\theta$. In this work, we extend this approach to more general spherically symmetric black holes (with spacetime metric $d{s}^2=g_{tt}d{t}^2+g_{rr}d{r}^2+g_{\theta \theta }d{\theta }^2+g_{\varphi \varphi }d{\varphi }^2$). Furthermore, it can be proved that our results from the geometric approach are completely equivalent to those from conventional approach based on effective potentials of test particles.

Acoustic black hole is becoming an attractive topic in recent years, for it open-up new direction for experimental/observational explorations of black holes. In this work, the gravitational bending of acoustic Schwarzschild black hole is investigated. The gravitational deflection angle of particles traveling along null geodesics, weak gravitational lensing and Einstein ring for acoustic Schwarzschild black hole are carefully studied and analyzed. Particularly, in the calculation of gravitational deflection angle, we resort to two approaches—the Gauss–Bonnet theorem and the geodesic method. The results show that the gravitational bending effect in acoustic Schwarzschild black hole is enhanced, compared with conventional Schwarzschild black hole. This result indicates that the acoustic black holes may be more easily detectable in gravitational bending effects and weak gravitational lensing observations.

The Compton scattering process plays significant roles in atomic and molecular physics, condensed matter physics, nuclear physics and material science. It could provide useful information on the electromagnetic interaction between light and matter. Several aspects of many-body physics, such us electronic structures, electron momentum distributions, many-body interactions of bound electrons, etc., can be revealed by Compton scattering experiments. In this work, we give a review of ab initio calculation of Compton scattering process. Several approaches, including the free electron approximation (FEA), impulse approximation (IA), incoherent scattering function/incoherent scattering factor (ISF) and scattering matrix (SM) are focused on in this work. The main features and available ranges for these approaches are discussed. Furthermore, we also briefly introduce the databases and applications for Compton scattering.

Photon sphere has attracted significant attention since the capture of black hole shadow images by Event Horizon Telescope. Recently, a number of studies have highlighted that the number of photon spheres and their distributions near black holes are strongly constrained by black hole properties. Specifically, for black holes with event horizons and proper asymptotic behaviors, the number of stable and unstable photon spheres satisfies the relation $$n_{\text {stable}} - n_{\text {unstable}} = -1.$$ n stable - n unstable = - 1 . In this study, we provide a new proof on this relation using a geometric analysis, which is carried out using intrinsic curvatures in the optical geometry of black hole spacetimes. Firstly, we demonstrate the existence of photon spheres near black holes assuming most general asymptotic behaviors (asymptotically flat black holes, asymptotically de-Sitter and anti-de-Sitter black holes). Subsequently, we prove that the stable and unstable photon spheres near black holes must be one-to-one alternatively separated from each other, such that each unstable photon sphere is sandwiched between two stable photon spheres (and each stable photon sphere is sandwiched between two unstable photon spheres). Our analysis in this study is applicable to any spherically symmetric black hole spacetimes.

The dark matter halo has non-negligible effects on the gravitational lensing of supermassive black hole in the galaxy center. Our work presents a study on the time-delay of light in gravitational lensing of black holes enclosed by dark matter halos. To provide a precise description on the distribution of dark matter in galaxies, we choose several famous phenomenological dark matter halo models in astrophysics, including the NFW, Beta, Burkert and Moore models, to carry out the present study. Through numerically calculating the time-delay of light in gravitational lensing, a comparative analysis of the dark matter effects within different halo models has been performed. Assuming typical length scales associated with the galactic gravitational lensing, numerical results indicate that the NFW, Beta, Burkert and Moore dark matter halos can significantly enhance the time delay of light in gravitational lenisng of central supermassive black holes. The enhancing effect becomes more pronounced with a small dark matter halo scale and an increasing dark matter halo mass.