Relativistic structure formation models and gravitoelectromagnetism
  In the framework of Lagrangian perturbation theory in general relativity we
discuss the possibility to split the Einstein equations, written in terms of
spatial Cartan coframes within a 3+1 foliation of spacetime, into
gravitoelectric and gravitomagnetic parts. While the former reproduces the full
hierarchy of the Newtonian perturbation solutions, the latter contains
non-Newtonian aspects like gravitational waves. This split can be understood
and made unique through the Hodge decomposition of Cartan coframe fields.
