Equivalence and Hermiticity of Dirac Hamiltonians in the Kerr gravitational field

Abstract

In the paper, for the Kerr field, we prove that Chandrasekhar's Dirac Hamiltonian and the self-adjoint Hamiltonian H_{\eta} with a flat scalar product of the wave functions are physically equivalent. Operators of transformation of Chandrasekhar's Hamiltonian and wave functions to the \eta-representation with a flat scalar product are defined explicitly. If the domain of the wave functions of Dirac's equation in the Kerr field is bounded by two-dimensional surfaces of revolution around the z axis, Chandrasekhar's Hamiltonian and the self-adjoint Hamiltonian in the \eta-representation are Hermitian with equality of the scalar products,(\psi, H \varphi)=(H \psi, \varphi).