## On the polarization of gravitational waves.(English)Zbl 1217.83027

Mladenov, Ivaïlo M. (ed.), Proceedings of the 9th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 8–13, 2007. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-42-4/pbk). 320-333 (2008).
A gravitational field that is invariant with respect to a non-Abelian two-dimensional Lie algebra whose generator is light like is characterized from a geometric point of view. It represents a spin-1 gravitational wave (of Petrov type $$N$$) propagating at light velocity. It is weaker than a spin-2 gravitational wave. Its metric in the harmonic coordinates has off-diagonal form and its (non-globally square integrable spin-1) perturbation has only one index in the plane orthogonal to the propagation direction. Non-singular spin-1 gravitational waves are those with a matter source.
Spin-1 gravitational waves are also analyzed using the gravitoelectromagnetic perspective, and the photon-photon gravitational interaction is also studied.
For the entire collection see [Zbl 1154.17001].

### MSC:

 83C35 Gravitational waves 83C20 Classes of solutions; algebraically special solutions, metrics with symmetries for problems in general relativity and gravitational theory 83C25 Approximation procedures, weak fields in general relativity and gravitational theory 83C50 Electromagnetic fields in general relativity and gravitational theory 83C10 Equations of motion in general relativity and gravitational theory