Can space have angular momentum that can be transfered to/from physical objects?

Question

This is related to another question that discusses whether space can have momentum and energy. Apparently gravitational waves or ripples in spacetime is how space stores and transfers energy/momentum.

Assume that space has two only two spheres with masses $m_0$ and $m_1$. If sphere with mass $m_0$ is suddenly imparted a rotation of velocity $\omega$, will the rotation somehow flow to the other sphere so that both rotate? If so, will both rotate in the same direction to ensure that the overall angular momentum is $m_0\omega$ or will they be opposed to make the overall angular momentum 0?

Answer 1

Comments to the question (v1):

1. In Newtonian mechanics with Newtonian gravity, a body can have orbital angular momentum wrt. a reference frame. A non-point-mass can also have spin angular momentum. Bodies can exchange angular momentum via tidal forces.

2. In GR, it possible to assign angular momentum to certain space-time regions (such as e.g. the Kerr space-times) and exchange angular momentum with e.g. matter test probes.

3. Finally, let us mention gravitoelectromagnetism, which is an approximation to GR. Here the EFE takes the form of Maxwell's equations, and a spin angular momentum plays the role of a magnetic dipole moment.