Bound States and Decay Times of Fermions in a Schwarzschild Black Hole Background

We compute the spectrum of normalized fermion bound states in a Schwarzschild black hole background. The eigenstates have complex energies. The real part of the energies, for small couplings, closely follow a Hydrogen-like spectrum. The imaginary contributions give decay times for the various states, due to the absorption properties of the hole. As expected, states closer to the hole have shorter half-lives. As the coupling increases, the spectrum departs from that of 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, which shifts to the 2P3/2 state. For each positive energy state a negative energy counterpart exists, with opposite sign of its real energy, and the same decay factor. It follows that the Dirac sea of negative energy states is decaying, which may provide a physical contribution to Hawking radiation. PACS numbers: 03.65.Ge, 04.70.Bw, 04.62.+v, 03.65.Pm