Particles in a stationary spherically symmetric gravitational field

Dirac's equation has been considered in a Schwarzschild (Reissner-Nordstrom) background. Resonances in a continuum of states are found, similar to the Klein-Gordon case. Also the solutions of the Dirac and Klein-Gordon equations are investigated for an extended gravitating source. Special attention has been given to the case in which the radius of the source tends towards its Schwarzschild radius. A limiting charge-to-mass ratio for black holes is obtained.