Spin-spin interaction is a fascinating class of gravitoelectromagnetic effect in which positive masses can interact in ways that appear to show an analogue of polarisation.
If we take two parallel discs and spin them on a common axis at the same speed (wrt the background stars), then they will be more strongly attracted to each other if they rotate in opposite directions than if they rotate in the same direction. This creates an analogue of the rule with electric charges or magnetic poles, that "opposite charges attract, like charges repel" but in this case, we have "Opposite spins attract, like spins repel". The analogy is stronger with magnetism, since each spinning body has to have two poles with opposite nominal polarity.
Justification for the effect
- If only one disc rotates, then it will feel a rotational GEM effect to both the background stars and to the parallel disc, which both have relative rotation.
- If the second disc rotates in lock-step with the first, there is then no relative rotation between the two, and the additional gravitomagnetic attraction that existed in the first situation disappears. (arguably, expressable as a repulsive effect compared to the first situation).
- If both disks rotate in opposite directions, then the rotational GEM attraction between them is stronger than if only one rotates, because the relative rotation is now even faster.
More advanced effects
In the previous section, the repulsive component between two parallel-rotating discs is "relative" to the case in which only one disc rotates. However, in a more nonlinear theory, we can imagine a scenario in which this repulsive antigravitational effect is real. If we visualise these situations in terms of twisted gravitational fieldlines, where the greater the twist, the more strongly intersected the region, and the stronger the attraction, then we can imagine the attraction between the contra-rotating discs as being due to the spatial linkages between atoms in the two discs being twisted up by the relative rotation creating a region with a more intense field, even though it contains the same number of fieldlines.
If we now consider the case of the pair of co-rotating discs, we can introduce the question of what might be called "gravitational transparency". For disc A, disc B seems to show an apparent outward radial gravitational field, and in a strongly nonlinear model, this field can deflect other gravitational fieldlines passing through the region, outwards, so that the background starfield seen by A through co-rotating disc B appears to show lensing effects.
Whether these further-generation effects are real or not, and whether they can be built on for practical metric engineering purposes, will require a more advanced theory than C20th GR.
- Robert Wald, Gravitational Spin Interaction Phys. Rev. D 6, 406, 15 July 1972 doi:10.1103/PhysRevD.6.406