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We present a full-sky derivation of weak lensing observables in thePost-Friedmann (PF) formalism. Weak lensing has the characteristic of mixingsmall scales and large scales since it is affected by inhomogeneitiesintegrated along the photon trajectory. With the PF formalism, we develop amodelling of lensing observables which encompasses both leading orderrelativistic effects and effects that are due to the fully non-linear matterdistribution at small scales. We derive the reduced shear, convergence androtation up to order $1/c^4$ in the PF approximation, accounting for scalar,vector and tensor perturbations, as well as galaxies' peculiar velocities. Wediscuss the various contributions that break the Kaiser-Squires relationbetween the shear and the convergence at different orders. We pay particularattention to the impact of the frame-dragging vector potential on lensingobservables and we discuss potential ways to measure this effect in futurelensing surveys.

Full-sky weak lensing: a nonlinear post-Friedmann treatment