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We present the first calculation of an intrinsically relativistic quantity infully non-linear cosmolog- ical large-scale structure studies. Traditionally,non-linear structure formation in standard {\Lambda}CDM cosmology is studiedusing N-body simulations, based on Newtonian gravitational dynamics on anexpanding background. When one derives the Newtonian regime in a way that is aconsistent ap- proximation to the Einstein equations, a gravito-magnetic vectorpotential - giving rise to frame dragging - is present in the metric inaddition to the usual Newtonian scalar potential. At leading order, this vectorpotential does not affect the matter dynamics, thus it can be computed fromNewtonian N-body simulations. We explain how we compute the vector potentialfrom simulations in {\Lambda}CDM and examine its magnitude relative to thescalar potential. We also discuss some possible observable effects.

Computing General Relativistic effects from Newtonian N-body simulations: Frame dragging in the post-Friedmann approach