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 ($m_gr \le1.62$) gives the same
result as GR, for large separations ($m_gr>1.62$) 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.
