Stationary bound states of Dirac particles in collapsar fields

It is the first time stationary bound states of elementary spin 1/2 particles that do not decay with time are obtained for a Schwarzschild gravitational field using a self-conjugate Hamiltonian with a flat scalar product in a wide range of gravitational coupling constant. In order to obtain a discrete energy spectrum, we introduce a boundary condition such that the current density of Dirac particles near the "event horizon" is zero.