Gravity Waves & Gravitomotive Force: Is Rotation Possible?

[snorkack]

For a binary emitting gravity waves: are there any directions of space into which gravity waves are not emitted for reasons of symmetry?
Also:
a steadily rotating electric charge current causes a magnetostatic field
A steadily rotating mass must cause a gravitomagnetostatic field.
Electrostatic field of an electric monopole charge is a potential field. Its integral through any closed circuit is zero.
A gravitostatic field of a mass monopole charge is also a potential field. Its integral through any closed circuit is also zero.
When a magnetic field varies in time, it causes electromotive field. It is electric field, but it is allowed to have nonzero integral through closed circuits.
What happens when gravitomagnetic field varies through time, for example due to orbital movement?
Can varying gravitomagnetic field include a gravitomotive field, with nonzero integral over closed circuits?
In other words, can varying gravitomagnetic field cause a wheel to rotate?

 

[PeterDonis]

There is a framework in which gravity is treated by analogy with electromagnetism:

https://en.wikipedia.org/wiki/Gravitoelectromagnetism

This framework has limitations: for example, it is not covariant under coordinate transformations, as Maxwell's equations are. So it cannot model gravitational radiation. But it does give a good idea of which EM effects have reasonably close gravitational analogues.

 

[snorkack]

So, repeating the first question:

For a binary emitting gravity waves: are there any directions of space into which gravity waves are not emitted for reasons of symmetry?

 

[pervect]

So, repeating the first question:

For a binary emitting gravity waves: are there any directions of space into which gravity waves are not emitted for reasons of symmetry?

I'd say yes, offhand, that there shouldn't be any GW emission in the directions in which the components of the quadrupole moment is constant. For instance, if the rotation is in the xy plane, and z is constant so that the integral of $z^2 dm$ is constant, I wouldn't expect any gravitational radiation in the z direction. But I don't have a rigorous proof, or a reference that says exactly this (Wiki and by memory several textbooks do say that you need a nonzero quadrupole moment to have gravitational radiation at all, but this doesn't quite say anything about the direction of the radiation).