  We compute the dipole of the galaxy correlation function at 1-loop in
perturbation theory by including all the relevant relativistic contributions.
This provides a description and understanding of what the dipole truly
measures, in particular in relation to the gravitational redshift effect in
Large Scale Structure. In order to develop this perturbative approach we have
computed for the first time the relevant relativistic corrections to third
order in perturbation theory, including the corresponding non-linear galaxy
bias model. This perturbative approach agrees on a wide range of scales with
good accuracy with previous numerical results based on geodesic light tracing
in N-body simulations. Previous claims of gravitational redshift detection may
have neglected several relativistic effects which are comparable with the
amplitude of gravitational redshift around 10 Mpc/h scales and which complicate
the gravitational redshift interpretation of the measurement.
