Comments on tensor analysis in generalized spacetimes

Abstract

The unique relationship between covariant and contravariant tensors that exists in general relativity no longer exists in generalized spacetimes with nonsymmetric metrics. The nature of covariant and contravariant tensors and their relationships in such spacetimes is clarified. An example is given to show that sensible field equations may be derived from a Lagrangian for such spacetimes, and that these equations differ nontrivially from general relativity. The physical applications of such a formalism are discussed.