Fermion absorption cross section of a Schwarzschild black hole

TL;DR

This paper investigates the quantum absorption cross section of a Schwarzschild black hole for massive spin-half particles, revealing quantum effects, oscillations, and convergence to classical and geometric-optics limits across different regimes.

Contribution

It provides a numerical analysis of fermion absorption by black holes, highlighting quantum violations of the equivalence principle and detailed behavior across various gravitational couplings and energies.

Findings

Cross section approaches classical results at high couplings.

Oscillations around the classical limit depend on particle mass.

Minimum cross section approaches  R_S^2/2 when the hole is much smaller than the wavelength.

Abstract

We study the absorption of massive spin-half particles by a small Schwarzschild black hole by numerically solving the single-particle Dirac equation in Painleve-Gullstrand coordinates. We calculate the absorption cross section for a range of gravitational couplings Mm/m_P^2 and incident particle energies E. At high couplings, where the Schwarzschild radius R_S is much greater than the wavelength lambda, we find that the cross section approaches the classical result for a point particle. At intermediate couplings 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 27 \pi R_S^2/4, 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 \pi R_S^2/2.