Spin–spin interactions in massive gravity and higher derivative gravity theories

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 (mgr⩽1.62mgr⩽1.62) gives the same result as GR, for large separations (mgr>1.62mgr>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.