The RayGalGroupSims cosmological simulation suite for the study of relativistic effects: an application to lensing-matter clustering statistics

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).