This situation changes in general relativity. There one has g ( p ) μ μ ν ν d x μ μ | p d x ν ν | p ( a , b ) = g ( p ) μ μ ν ν a μ μ b ν ν , where now η → g (p), i.e., g is still a metric tensor but now depending on spacetime and is a solution of Einstein's field equations. Moreover, a, b must be tangent vectors at spacetime point p and can no longer be moved around freely.