The greybody factor for the monopole and odd-parity modes of the Proca field in the Schwarzschild black hole spacetimes

Abstract

The greybody factor is one of the famous results of the black hole perturbation theory, which describes the transmission probability of a particle radiated by a black hole into spatial infinity. In this work, we separated the angular parts of the equations of motion and derived the radial equations for the Proca field in the Schwarzschild black hole spacetime. The radial equations for the monopole and odd-parity modes are fully decoupled in the Schrödinger-like form. We study the greybody factor by determining the rigorous bound.