Mathematical Physics and Quantum Field Theory
Electron. J. Diff. Eqns., Conf. 04, 2000, pp. 75-85.

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

J. D. Finley, III

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 physical origins of the problem are briefly described. The problem arises out of searches for Bäcklund transforms of a system of PDE's that describe twisting, Petrov type N solutions of Einstein's vacuum field equations.

Published July 12, 2000.
Mathematics Subject Classifications: 17B80, 37K10, 17B66, 83C35.
Key words: Backlund transformations, Einstein equations, gravitational waves.

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J. D. Finley, III
Dept. of Physics and Astronomy
University of New Mexico
Albuquerque, NM 87131

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