On Dirac's Wave Equation in a Gravitational Field

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Abstract
The Dirac equation is investigated in the combined electric and gravitational field of a point charge in General Relativity. The wavefunctions are weakly singular at the origin, but still normalizable for a continuous range of the energy. The Hamiltonian, however, is not self‐adjoint over the manifold of its own ``eigenstates,'' though it can be made self‐adjoint by a suitable choice of its domain of definition. The theory, however, is unable to decide how the Hamiltonian should be defined, and what are the bound states.