  We investigate the corrections which relativistic light-cone computations
induce on the correlation of the tangential shear with galaxy number counts,
also known as galaxy-galaxy lensing. The standard-approach to galaxy-galaxy
lensing treats the number density of sources in a foreground bin as observable,
whereas it is in reality unobservable due to the presence of relativistic
corrections. We find that already in the redshift range covered by the DES
first year data, these currently neglected relativistic terms lead to a
systematic correction of up to 50% in the density-shear correlation function
for the highest redshift bins. This correction is dominated by the the fact
that a redshift bin of number counts does not only lens sources in a background
bin, but is itself again lensed by all masses between the observer and the
counted source population. Relativistic corrections are currently ignored in
the standard galaxy-galaxy analyses, and the additional lensing of a counted
source populations is only included in the error budget (via the covariance
matrix). At increasingly higher redshifts and larger scales, these relativistic
and lensing corrections become however increasingly more important, and we here
argue that it is then more efficient, and also cleaner, to account for these
corrections in the density-shear correlations.
