  If Einstein's equations are to describe a field theory of gravity in
Minkowski spacetime, then causality requires that the effective curved metric
must respect the flat background metric's null cone. The kinematical problem is
solved using a generalized eigenvector formalism based on the Segr\'{e}
classification of symmetric rank 2 tensors with respect to a Lorentzian metric.
Securing the correct relationship between the two null cones dynamically
plausibly is achieved using the naive gauge freedom. New variables tied to the
generalized eigenvector formalism reduce the configuration space to the
causality-respecting part. In this smaller space, gauge transformations do not
form a group, but only a groupoid. The flat metric removes the difficulty of
defining equal-time commutation relations in quantum gravity and guarantees
global hyperbolicity.
