  Gravitational waves astronomy has opened a new opportunity to study the
Universe. Full exploitation of this window can especially be provided by
combining data coming from gravitational waves experiments with luminous
tracers of the Large Scale Structure, like galaxies. In this work we
investigate the cross-correlation signal between gravitational waves resolved
events, as detected by the Einstein Telescope, and actively star-forming
galaxies. The galaxies distribution is computed through their UV and IR
luminosity functions and the gravitational waves events, assumed to be of
stellar origin, are self-consistently computed from the aforementioned galaxies
distribution. We provide a state-of-the-art treatment both on the astrophysical
side, taking into account the impact of the star formation and chemical
evolution histories of galaxies, and in computing the cross-correlation signal,
for which we include lensing and relativistic effects. We find that the
measured cross-correlation signal can be sufficiently strong to overcome the
noise and provide a clear signal. As a possible application of this
methodology, we consider a proof-of-concept case in which we aim at
discriminating a metallicity dependence on the compact objects merger
efficiency against a reference case with no metallicity dependence. When
considering galaxies with a Star Formation Rate $\psi > 10 \: M_{\odot}
/\rm{yr}$, a Signal-to-Noise ratio around a value of 2-4 is gained after a
decade of observation time, depending on the observed fraction of the sky. This
formalism can be exploited as an astrophysical probe and could potentially
allow to test and compare different astrophysical scenarios.
