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Abstract:
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 that involve only finite products of the unknowns and their
derivatives. Considerable additional simplifications arise in physically interesting cases where metrics
become 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 that 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.
