General features of spacetime

Abstract

A fundamental assumption of the general theory of relativity is that the physical spacetime is a four-dimensional manifold with a non-degenerate metric 〈,〉 of signature +2. Signature of the metric is the number of positive eigenvalues of metric components matrix gμν minus the number of its negative eigenvalues. As the metric is non-degenerate, there can be no zero eigenvalues. This statement is independent of coordinate system chosen. The actual numerical values of eigenvalues of the tensor matrix may vary from one coordinate system to another but the number of eigenvalues of positive sign and of negative sign is the same.