Escape probability for isotropic emitters near Kerr black hole with astrometric

The paper investigates the escape probability for isotropic emitters near a Kerr black hole. We propose a new approach to obtain the escape probability in a general manner, going beyond previous case-by-case studies. This approach is based on studies of the black hole shadow with astrometric observable and can be applied to emitters with an arbitrary 4-velocities and locations, even to the emitters outside of the equatorial plane. We also consider representative examples illustrating how escape probabilities vary with distance, velocity, and inclination angle. Overall, this new approach provides an effective method for studying escape probabilities near Kerr black holes.