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.

In the original version of this article, the last name of the second author missed its last letter.