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(E) for a range of gravitational couplings Mm/mP 2 and incident particle energies E. At high couplings, where the Schwarzschild radius RS is much greater than the wavelength λ, we find that σ(E) approaches the classical result for a point particle. At intermediate couplings, RS ∼ λ, we find oscillations around the classical limit whose precise form depends on the particle mass. These oscillations give quantum violations of the equivalence principle. At high energies the cross section converges on the geometric-optics value of 27πR S/4, and at low energies we find agreement with an approximation derived by Unruh. When the hole is much smaller than the particle wavelength we confirm that the minimum possible cross section approaches πR S/2. PACS numbers: 04.70.Bw, 03.80.+r, 04.62.+v, 03.65.Pm