A Note on the Sagnac Effect for Matter Beams
  We study the Sagnac effect for matter beams, in order to estimate the kinematic corrections to the basic formula, deriving from the position and the extent of the interferometer, and discuss the analogy with the Aharonov-Bohm effect. We show that the formula for the Sagnac time delay is the same for matter and light beams in arbitrary stationary space-times, provided that a suitable condition on the speed of the beams is fulfilled. Hence, the same results obtained for light beams apply to matter beams. 
Matteo Luca Ruggiero, Angelo Tartaglia
gr-qc