Dept. of Physics and Astronomy
University of New Mexico
Albuquerque, NM 87131
e-mail: finley@tagore.phys.unm.edu
J. D. Finley, III
Abstract:
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 e-mail: finley@tagore.phys.unm.edu |