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The new potential for the Weyl tensor in N dimensions: gauge andwave equation

Published online by Cambridge University Press:  30 September 2008

S. Brian Edgar
Affiliation:
Matematiska Institutionen, Linköpings Universitet, 581 83, Linköping, Sweden
J.M.M. Senovilla
Affiliation:
Física Teórica, Universidad del País Vasco, Apartado 644, 48080 Bilbao, Spain
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Abstract

Although the Lanczos potential (a (2,1) form, Labc) for theWeyl tensor does not exist in dimensions greater than four, a newpotential (a (2,3) form, Pabcde, which coincides with thedouble dual of Labc in four dimensions) has recently beenshown to exist in all dimensions n ≥ 4.In this talk we investigate the question of gauge and discuss the structure of the new potential's wave equation whichis obtained from the Bianchi identities; identifying the gauge supplies us with a new direct proof of the existence of Pabcde via the Cauchy-Kowaleski theorem, as well as the foundation for more general investigations of the first order symmetric hyperbolic structure.

Type
Research Article
Copyright
© EAS, EDP Sciences, 2008

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References

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