  Many of the technical complications associated with the general theory of
relativity ultimately stem from the nonlinearity of Einstein's equation. It is
shown here that an appropriate choice of dynamical variables may be used to
eliminate all such nonlinearities beyond a particular order: Both
Landau-Lifshitz and tetrad formulations of Einstein's equation are obtained
which involve only finite products of the unknowns and their derivatives.
Considerable additional simplifications arise in physically-interesting cases
where metrics becomes approximately Kerr or, e.g., plane waves, suggesting that
the variables described here can be used to efficiently reformulate
perturbation theory in a variety of contexts. In all cases, these variables are
shown to have simple geometrical interpretations which directly relate the
local causal structure associated with the metric of interest to the causal
structure associated with a prescribed background. A new method to search for
exact solutions is outlined as well.
