Effective low-energy gravitational potential for slow fermions coupled to linearized massive gravity

We analyze the Dirac equation for slow fermions coupled to linearized massive gravity above the Minkowski background and derive the effective low-energy gravitational potential. The obtained results can be used in terrestrial laboratories for the detection of gravitational waves and fluxes of massive gravitons emitted by cosmological objects. We also calculate the neutron spin precession within linearized massive gravity, which in principle can be measured by neutron interferometers.