Weak-lensing observables in relativistic N-body simulations
  We present a numerical weak-lensing analysis that is fully relativistic and
non-perturbative for the scalar part of the gravitational potential and
first-order in the vector part, frame dragging. Integrating the photon
geodesics backwards from the observer to the emitters, we solve the Sachs
optical equations and study in detail the weak-lensing convergence, ellipticity
and rotation. For the first time, we apply such an analysis to a
high-resolution relativistic N-body simulation, which consistently includes the
leading-order corrections due to general relativity on both large and small
scales. These are related to the question of gauge choice and to post-Newtonian
corrections, respectively. We present the angular power spectra and one-point
probability distribution functions for the weak-lensing variables, which we
find are broadly in agreement with comparable Newtonian simulations. Our
geometric approach, however, is more robust and flexible, and can therefore be
applied consistently to non-standard cosmologies and modified theories of
gravity.
