Gravitomagnetic response of an irrotational body to an applied tidal field

The deformation of a nonrotating body resulting from the application of a tidal field is measured by two sets of Love numbers associated with the gravitoelectric and gravitomagnetic pieces of the tidal field, respectively. The gravitomagnetic Love numbers were previously computed for fluid bodies, under the assumption that the fluid is in a strict hydrostatic equilibrium that requires the complete absence of internal motions. A more realistic configuration, however, is an irrotational state that establishes, in the course of time, internal motions driven by the gravitomagnetic interaction. We recompute the gravitomagnetic Love numbers for this irrotational state, and show that they are dramatically different from those associated with the strict hydrostatic equilibrium: While the Love numbers are positive in the case of strict hydrostatic equilibrium, they are negative in the irrotational state. Our computations are carried out in the context of perturbation theory in full general relativity, and in a post-Newtonian approximation that reproduces the behavior of the Love numbers when the body's compactness is small.