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Note on the Physical Interpretation of Chandrasekhar's Separation Constants in his Solution of Dirac's Equation in Kerr Geometry

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...

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Bibliographic Details
Published in:Proceedings of the Royal Society of London. Series A, Mathematical and physical sciences Mathematical and physical sciences, 1989-08, Vol.424 (1867), p.323-326
Main Author: Pekeris, C. L.
Format: Article
Language:English
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Summary: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 eimp, 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.
ISSN:1364-5021
0080-4630
1471-2946
2053-9169
DOI:10.1098/rspa.1989.0086