Main Question or Discussion Point
In considering special relativity as a limiting case of the general theory (without matter or curvature) the question arose as to whether the pseudo-riemann nature of the SR metric is actually an independant (essentially experimentally determined) assumption/property or derivable from the structure of the general theory. Can someone clarify if a positive-definite metric GR theory can be constructed which would still accurately describe the basic properties of matter/gravity via space-time curvature? Obviously the observed properties of nature (eqivalent reference frames, constancy of speed of light) dictate a pesudo-riemann metric, I'm just wondering if this is an independent assumption or 'baked into' the mathematical structure of the general theory. Many thanks!