  We consider a boundary value problem for the Dirac equation in a smooth,
asymptotically flat Lorentzian manifold admitting a Killing field which is
timelike near and tangential to the boundary. A self-adjoint extension of the
Dirac Hamiltonian is constructed. Our results also apply to the situation that
the space-time includes horizons, where the Hamiltonian fails to be elliptic.
