Local existence of symmetric spinor potentials for symmetric (3,1)-spinors in Einstein space-times

• 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'H BC)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. © 2001 Elsevier Science B.V.

Nyckelord

02.40

04.20.Ex

81R25

83C15

Cauchy problem

General relativity

Lanczos potential

Spinors and twistors

Wave equation

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