Fermion absorption cross section of a Schwarzschild black hole

We study the absorption of massive spin-half particles by a small Schwarzschild black hole by numerically solving the single-particle Dirac equation in Painlevé-Gullstrand coordinates. We calculate the absorption cross section σ over a range of gravitational couplings Mm/m_P² and incident particle energies E. At high couplings, where the Schwarzschild radius R_S is much greater than the particle wavelength λ, we find that σ(E) approaches the classical result for a point particle. At intermediate couplings, where R_S∼λ, we find oscillations around the classical limit whose precise form depends on the particle mass. At low couplings, where R_S≪λ, we demonstrate that the minimum-possible cross section approaches πR_S²/2. For high incident particle energies, the cross section converges on the geometric-optics value of 27πR_S²/4. At low particle energies we find agreement with an approximation derived by Unruh.