Detecting the Angular Momentum of the Galactic Dark Halo

General relativity predicts the presence of a gravito-magnetic component of the gravitational interaction induced by a rotating mass. It is currently assumed that our galaxy (as well as the others) is immersed in a dark halo. If so, it is reasonable to expect the halo to rotate, then to produce a gravito- magnetic field. Here we present a proposal to measure such effect exploiting the fully relativistic version of the Sagnac effect. When an electromagnetic signal is led to travel along a spacely closed path immersed in a gravito- magnetic field the time of flight for a complete turn depends on the direction of rotation. The proposed physical loop would be based on the Lagrange points of the Sun-Earth pair. An evaluation of the sensitivity of such a measurement, together with a discussion of more opportunities that the experiment would offer is also presented.