Effect of scalar mass in the absorption and emission spectra of Schwarzschild black hole

Following Sanchez's approach we investigate the effect of scalar mass in the absorption and emission problems of a four-dimensional (4D) Schwarzschild black hole. The absorption cross sections for arbitrary angular momentum of the scalar field are computed numerically in the full range of energy by making use of the analytic near-horizon and asymptotic solutions and their analytic continuations. The scalar mass has an interesting effect in the low-energy absorption cross section for the S-wave. Unlike the massless case, the cross section decreases with increasing energy in the extremely low-energy regime. As a result the universality, i.e., low-energy cross section for the S-wave is equal to the horizon area, is broken in the presence of mass. If the scalar mass is larger than the critical mass, the absorption cross section becomes a monotonically decreasing function in the entire range of energy. The Hawking emission is also calculated numerically. It turns out that the Planck factor generally suppresses the contribution of higher partial waves except the S-wave. The scalar mass in general tends to reduce the emission rate.