Locally Metric Spacetimes
arXiv:0804.2911
Abstract
Spacetimes have conventionally been described by a global Lorentzian metric on a differentiable four-manifold. Herein we explore the possibility of spacetimes defined by a connection, which is locally but not globally Levi-Civita. The general method of obtaining such connections is presented for the non-degenerate case followed by an example that modifies the Robertson-Walker spacetimes for flat spacelike hypersurfaces.
16 pages