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 lengthparameter a, Chandrasekhar's separation constant λ is equal to ±(j + 1/2)/surd 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_{+1/2}(θ,\varphi) and S_{1/2}(θ,\varphi), 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 Schrodinger and by Pauli, in which the dependence of all four spinors on the azimuthal variable \varphi is given by the single factor of e^{im\varphi}, 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.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 August 1989
 DOI:
 10.1098/rspa.1989.0086
 Bibcode:
 1989RSPSA.424..323P