Full-sky weak lensing: a nonlinear post-Friedmann treatment
  We present a full-sky derivation of weak lensing observables in the
Post-Friedmann (PF) formalism. Weak lensing has the characteristic of mixing
small scales and large scales since it is affected by inhomogeneities
integrated along the photon trajectory. With the PF formalism, we develop a
modelling of lensing observables which encompasses both leading order
relativistic effects and effects that are due to the fully non-linear matter
distribution at small scales. We derive the reduced shear, convergence and
rotation up to order $1/c^4$ in the PF approximation, accounting for scalar,
vector and tensor perturbations, as well as galaxies' peculiar velocities. We
discuss the various contributions that break the Kaiser-Squires relation
between the shear and the convergence at different orders. We pay particular
attention to the impact of the frame-dragging vector potential on lensing
observables and we discuss potential ways to measure this effect in future
lensing surveys.
