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