We show that , in the weak field limit , at large separations , in sharp contrast to General Relativity ( GR ) , all massive gravity theories predict distance-dependent spin alignments for spinning objects .
For all separations GR requires anti-parallel spin orientations with spins pointing along the line joining the sources .
Hence total spin is minimized in GR .
On the other hand , while massive gravity at small separations ( m _ { g } r \leq 1.62 ) gives the same result as GR , for large separations ( m _ { g } r > 1.62 ) the spins become parallel to each other and perpendicular to the line joining the objects .
Namely , the potential energy is minimized when the total spin is maximized in massive gravity for large separations .
We also compute the spin-spin interactions in quadratic gravity theories and find that while at large separations GR result is intact , at small separations , spins become perpendicular to the line joining sources and anti-parallel to each other .