Could gravity around rotating bodies make them pull apart rather than attract? Due to the gravitational field analogous to the magnetic field

In this video:

Eugene explains that moving bodies generate two types of gravitational fields, the common one that attracts other bodies as we usually study gravitation in classical physics, and another similar to a magnetic field due to movement.

This new gravitational field is necessary because of relativity and how electromagnetism works, it is the explanation of how two observers agree on the result of some experiments involving gravity and electromagnetism.

I was surprised to find that the force generated by this new gravitational field is repulsive. A repulsive "gravitational" force. So I tried to imagine a scenario where this force would be able to make electrically neutral bodies repel each other gravitationally, instead of attracting each other.

I noticed that due to the similarity of this field with the magnetic field, a very massive rotating body would generate a "gravitomagnetic" field around itself, similar to the magnetic field that the Earth generates around itself, which has poles (north and south).

If two equal magnetic poles are placed close together, they repel each other, therefore, I imagined that if two equally massive bodies, rotating in the same direction, were placed close together, in such a way that their equal poles approached each other, they would repel each other, just like magnets do, however, due to their mass and rotation.

Is this correct?

I have doubts if so because I believe that this field analogous to the magnetic can be just an artifice so that measurements from different observers agree, and therefore, if two neutral massive bodies repel each other, it will be impossible for someone in "relative rest" to agree on the cause of this repulsion since, in the view of this observer, this field does not exist.

• I watched the video. There's a disclaimer in it that this view of gravity is just an approximation of what goes on in GR and isn't valid at relativistic speeds (the exact domain they used to show there should be this repulsive force). I'm going to nip this in the bud. Gravity doesn't have a repulsive component. Applying regular gravity to SR causes paradoxes, but those are solved without a repulsive component by using the proper formulation. In fact, the video gives the proper explanation after talking about gravity waves. The electric force increases. The rest was click-bait sensationalizing.
– Jim
Commented Jan 25, 2022 at 21:10