Essential self-adjointness of Dirac operators under the influence of general-relativistic gravity

Physical reasoning gives expressions for the hamiltonian of a system of quantum-mechanical particles. These hamiltonians are often differential operators that are symmetric in a densely-defined domain. However, to study the dynamics of the unitary group corresponding to a hamiltonian, it is required that the hamiltonian be self-adjoint or essentially self-adjoint. This study analyzes the effect of the static non-linear electromagnetic-vacuum spacetime of a point nucleus on the self-adjointness and the spectrum of the general-relativistic Dirac hamiltonian for a test electron.