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Inelastic scattering of electrons by black hole atoms

Electron-impact inelastic scattering processes involving black hole atoms are calculated by direct solution of the general relativistic Klein–Gordon equation. In Eddington–Finkelstein coordinates for the space-time metric, the Hamiltonian is non-singular, complex and non- Hermitian. Bound states of an electron and a black hole with a mass of 3.8 × 1012 kg and 3.8 × 1013 kg are found by matrix diagonalization of the time-independent Klein–Gordon equation. Absorption effects on inelastic scattering of electrons by a black hole atom are investigated by comparing solutions of the time-dependent Klein–Gordon equation with and without general relativistic corrections to the Newtonian gravitational potential. As the black hole becomes more massive, the absorption effects on the inelastic scattering become more pronounced.