  General Relativistic effects on the clustering of matter in the universe
provide a sensitive probe of cosmology and gravity theories that can be tested
with the upcoming generation of galaxy surveys. Here, we present a suite of
large volume high-resolution N-body simulations specifically designed to
generate light-cone data for the study of relativistic effects on
lensing-matter observables. RayGalGroupSims (or in short RayGal) consists of
two N-body simulations of $(2625\,h^{-1}\,{\rm Mpc})^3$ volume with $4096^3$
particles of a standard flat $\Lambda$CDM model and a non-standard $w$CDM
phantom dark energy model. Light-cone data from the simulations have been
generated using a parallel ray-tracing algorithm that has accurately solved
billion geodesic equations. Catalogues and maps with relativistic weak-lensing
which include post-Born effects, magnification bias (MB) and redshift space
distortions (RSD) due to gravitational redshift, Doppler, transverse Doppler,
Integrated Sachs-Wolfe/Rees-Sciama effects, are publicly released. Using this
dataset, we are able to reproduce the linear and quasi-linear predictions from
the Class relativistic code for the 10 (cross-)power spectra (3$\times$2
points) of the matter density fluctuation field and the gravitational
convergence at $z=0.7$ and $z=1.8$. We find $1-30\%$ level contribution from
both MB and RSD to the matter power spectrum, while the Fingers-of-God effect
is visible at lower redshift in the non-linear regime. MB contributes at the
$10-30\%$ level to the convergence power spectrum leading to a deviation
between the shear power-spectrum and the convergence power-spectrum. MB also
plays a significant role in the galaxy-galaxy lensing by decreasing the
density-convergence spectra by $20\%$, while coupling non-trivial
configurations (such as the one with the convergence at the same or even lower
redshift than the density field).
