The oft-neglected issue of the causal structure in the flat spacetime
approach to Einstein's theory of gravity is considered. Consistency requires
that the flat metric's null cone be respected, but this does not happen
automatically. After reviewing the history of this problem, we introduce a
generalized eigenvector formalism to give a kinematic description of the
relation between the two null cones, based on the Segre' classification of
symmetric rank 2 tensors with respect to a Lorentzian metric. Then we propose a
method to enforce special relativistic causality by using the naive gauge
freedom to restrict the configuration space suitably. A set of new variables
just covers this smaller configuration space and respects the flat metric's
null cone automatically. In this smaller space, gauge transformations do not
form a group, but only a groupoid. Respecting the flat metric's null cone
ensures that the spacetime is globally hyperbolic, indicating that the Hawking
black hole information loss paradox does not arise.Comment: groupoid nature of gauge transformations explained; shortened, new
references, 102 page
