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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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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 |
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Main Author: | |
Format: | Article |
Language: | English |
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Citations: | Items that this one cites |
Online Access: | Get full text |
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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. |
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ISSN: | 1364-5021 0080-4630 1471-2946 2053-9169 |
DOI: | 10.1098/rspa.1989.0086 |