On the Eigenvalue Problem of the Dirac Hamiltonian in a Singular Spacetime Background

M. Martinis, N.Perkovic

We studied the motion of a spin onehalf particle in a singular spacetime metric of exponential type. This singular spacetime metric is obtained from a particular interpretation of the Newtonian gravitational force. For a given energy, the motion of a particle is described by the eigenvalue modes of the Dirac operator in a singular space time metric of exponential type. In this paper only the first order solution is considered leading to a cubic algebraic equation for energy eigenvalue. A novel interpretation for a gravitational atom is obtained.