Twisting gravitational waves and eigenvector fields for SL(2,C) on an infinite jet *

J Finley
2000 Mathematical Physics and Quantum Field Theory, Electronic Journal of Differential Equations, Conf. 04   unpublished
A system of coupled vector-field-valued partial differential equations is presented, the solutions to which would determine two coupled, infinite-dimensional vector-field realizations of the group SL(2,C). While the general solution is (partially) presented, the complicated nature of that solution is deplored, and the hope expressed that someone can replace it by something much more natural. The problem arises out of searches for Bäcklund transforms of a system of PDE's that describe twisting,
more » ... describe twisting, Petrov type N solutions of Einstein's vacuum field equations.