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We compute the spectrum of normalizable fermion bound states in aSchwarzschild black hole background. The eigenstates have complex energies. Thereal part of the energies, for small couplings, closely follow a hydrogen-likespectrum. The imaginary parts give decay times for the various states, due tothe absorption properties of the hole, with states closer to the hole havingshorter half-lives. As the coupling increases, the spectrum departs from thatof the hydrogen atom, as states close to the horizon become unfavourable.Beyond a certain coupling the 1S1/2 state is no longer the ground state, whichshifts to the 2P3/2 state, and then to states of successively greater angularmomentum. For each positive energy state a negative energy counterpart exists,with opposite sign of its real energy, and the same decay factor. It followsthat the Dirac sea of negative energy states is decaying, which may provide aphysical contribution to Hawking radiation.Comment: 27 pages, 14 figures, fully revised versio

Bound states and decay times of fermions in a Schwarzschild black hole background