## Twisting gravitational waves and eigenvector fields for $$\text{SL}(2,\mathbb C)$$ on an infinite jet.(English)Zbl 1055.83012

Summary: 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 $$\text{SL}(2,\mathbb C)$$. 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.

### MSC:

 83C35 Gravitational waves 83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory
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