Dark gravitomagnetism with LISA and gravitational waves space detectors

We present here the proposal to use the LISA interferometer for detecting the gravitomagnetic field due to the rotation of the Milky Way, including the contribution given by the dark matter halo. The galactic signal would be superposed to the gravitomagnetic field of the Sun. The technique to be used is based on the asymmetric propagation of light along the closed contour of the space interferometer (Sagnac-like approach). Both principle and practical aspects of the proposed experiment are discussed. The strategy for disentangling the sought for signal from the kinematic terms due to proper rotation and orbital motion is based on the time modulation of the time of flight asymmetry. Such modulation will be originated by the annual oscillation of the plane of the interferometer with respect to the galactic plane. Also the effect of the gravitomagnetic field on the polarization of the electromagnetic signals is presented as an in principle detectable phenomenon.