Local existence of symmetric spinor potentials for symmetric (3,1)-spinors in Einstein space–times |
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Authors: | F Andersson SB Edgar |
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Institution: | a Department of Mathematics, Linköping University, S581 83 Linköping, Sweden |
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Abstract: | We investigate the possibility of existence of a symmetric potential HABA′B′=H(AB)(A′B′) for a symmetric (3,1)-spinor LABCA′, e.g., a Lanczos potential of the Weyl spinor, as defined by the equation LABCA′= (AB′HBC)A′B′. We prove that in all Einstein space–times such a symmetric potential HABA′B′ exists. Potentials of this type have been found earlier in investigations of some very special spinors in restricted classes of space–times. A tensor version of this result is also given. We apply similar ideas and results by Illge to Maxwell’s equations in a curved space–time. |
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Keywords: | Lanczos potential Wave equation Cauchy problem |
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