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The Weyl-Lanczos Equations and the Lanczos Wave Equation in 4 Dimensions as Systems in Involution

P. Dolan·A. Gerber
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Abstract

Using the work by Bampi and Caviglia, we write the Weyl-Lanczos equations as an exterior differential system. Using Janet-Riquier theory, we compute the Cartan characters for all spacetimes with a diagonal metric and for the plane wave spacetime since all spacetimes have a plane wave limit. We write the Lanczos wave equation as an exterior differential system and, with assistance from Janet-Riquier theory, we find that it forms a system in involution. This result can be derived from the scalar wave equation itself. We compute its Cartan characters and compare them with those of the Weyl-Lanczos equations.

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P. Dolan, A. Gerber. 2003-01-23. The Weyl-Lanczos Equations and the Lanczos Wave Equation in 4 Dimensions as Systems in Involution. https://doi.org/10.1063/1.1566096

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