  We demonstrate that a slowly rotating compact body subjected to a stationary
tidal field undergoes a dynamical response, in which the fluid variables and
the interior metric vary on the time scale of the rotation period. This
dynamical response requires the tidal field to have a gravitomagnetic component
generated by external mass currents; the response to a gravitoelectric tidal
field is stationary. We confirm that in a calculation carried out to first
order in the body's rotation, the exterior geometry bears no trace of this
internal dynamics; it remains stationary in spite of the time-dependent
interior.
