In gravity (GR) apparently there are forces which occur which are related to the spin of two masses.
For example if we had a rotating gravitational source and dropped, say, some particles into it with instrinsic spin, they would fall differently under gravity.
From what we learned at school, every object no matter what it's made of must fall the same under gravity. It only depends on the mass of the source. (i.e. drop a feather and a rock they must fall the same on the moon).
So was Galileo wrong?
What's more, using this spin-spin interaction seems to suggest that one might use this interaction to create an anti-gravity device. (In the sense that one could create an object that fell every so slightly slower towards a spinning object such as the sun or Earth).
In fact I've seen papers which suggest that two spinnning black holes could even repel each other.
Since gravity is equivalent to acceleration, is there an equivalent accelerated frame that causes different spinning particles to behaving differently?
I'm trying to reconcile this spin-spin interaction with what I was previously taught about how things must fall the same under gravity.