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

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

2002-12-12

arxiv.org/abs/gr-qc/0212056v2

J.Math.Phys. 44 (2003) 3035-3045

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, latex, no figures, references corrected

Scientific paper

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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