  We consider the presence of odd powers of the speed of light $c$ in the
covariant nonrelativistic expansion of General Relativity (GR). The term of
order $c$ in the relativistic metric is a vector potential that contributes at
leading order in this expansion and describes strong gravitational effects
outside the (post-)Newtonian regime. The nonrelativistic theory of the leading
order potentials contains the full non-linear dynamics of the stationary sector
of GR.
