Note on the physical interpretation of Chandrasekhar’s separation constants in his solution of Dirac’s equation in Kerr geometry

Abstract

It is shown that in the limit of vanishing Kerr length-parameter a, Chandrasekhar’s separation constant λ is equal to ± ( j + ½ )/√2, where j is the total angular momentum. This result is derived from a comparison of the form of the simultaneous partial differential equation obeyed by Chandrasekhar’s angular functions, S +½ (θ, φ) and S -½ (θ, φ), with the differential equations obeyed by the corresponding pair of angular functions in flat space. The latter are taken from the solution of Dirac’s equation given by Schrödinger and by Pauli, in which the dependence of all four spinors on the azimuthal variable φ is given by the single factor of e imp , as in Chandrasekhar’s solution. For finite values of a, one can use the analytic expansion of λ in powers of a given by Pekeris & Frankowski.