Non–metric Spacetimes Typeset Using Revt E X 1

An example of homogeneous space which has no metric but has a connection with non–vanishing curvature suggests that " spacetime " should be not defined as a pair (M, g), a manifold plus a metric, but as a pair (M, Γ) — a differentiable manifold plus a connection. The general theory of homogeneous spaces ensures the existence of a certain well–defined connection independently of the existence of a metric. In the standard General Rela-tivistic case for homogeneous spaces, this connection is the usual Christoffel connection.