Light rings and shadows of static black holes in effective quantum gravity

Recently, two types of static black hole models that retain general covariance have been proposed within the Hamiltonian constraint approach to effective quantum gravity (EQG). We have studied the light rings and shadows of these black holes using the topological method and the backward ray-tracing method, respectively. We demonstrate that these light rings in both types of static black holes are standard and unstable according to the classification of light rings. Subsequently, we checked the position of the light rings using the photon trajectory equation. We found that although the quantum parameters do not affect the light rings of these two types of black holes, they do reduce the size of the first type of static black hole in EQG, making it smaller. However, for the second type of static black hole in EQG, we cannot distinguish it from a Schwarzschild black hole based on the shadow alone. Fortunately, the quantum parameters shrink the lensing rings of both types of black holes in EQG, causing the black hole shadow to occupy a larger proportion within the ring. This can serve as a basis for distinguishing whether the black hole is in EQG or general relativity (GR).