Quasibound states of the Dirac field in Schwarzschild and Reissner–Nordström black hole backgrounds

Abstract

In this paper, we study the existence of (quasi)bound states in two spacetime geometries describing Schwarzschild and Reissner–Nordström black holes. For obtaining these types of states, we search for discrete quantum modes of the massive Dirac equation in the two geometries. After imposing the quantization condition, an analytical expression for the energy of the ground states is derived. The energy of higher states is then obtained numerically. For very small values of the black hole mass M, we compare the energy of the Reissner–Nordström black hole quasibound state with the Dirac–Coulomb energy and we have found the two to be in good agreement.