Absorption, scattering, geodesics, shadows and lensing phenomena of black holes in effective quantum gravity

In this work, we investigate the signatures of black holes within an effective quantum gravity framework recently proposed in the literature (Cong et al., 2024). We begin by outlining the general setup, highlighting the two distinct models under consideration. This includes a discussion of their general properties, interpretations, and the structure of the event and inner horizons. We then examine the behavior of light in this context, analyzing geodesics, the photon sphere, and shadow formation. To validate our results, we estimate lower bounds for the shadow radius based on observational data from Sgr A${}^{\ast }$ and M87${}^{\ast }$. Subsequently, we derive the partial radial wave equation for scalar perturbations, enabling us to study the absorption cross-section in both low- and high-frequency regimes. Additionally, we evaluate the greybody factors and provide bounds for both bosonic and fermionic fields. Finally, we present a detailed analysis of gravitational lensing in both the weak and strong deflection limits. For the weak deflection regime, the Gauss–Bonnet theorem is employed, while for the strong deflection limit, the Tsukamoto approach is utilized.