> (local) Lorentz invariance This is also very misleading terminology, as curvature is a local invariant of a (semi) Riemannian manifold. Lorentz invariance i

> (local) Lorentz invariance This is also very misleading terminology, as curvature is a local invariant of a (semi) Riemannian manifold. Lorentz invariance is violated locally, even though the “magnitude” of this violation goes to zero if the volume of the neighborhood goes to zero. > In General Relativity, Lorentz invariance is what you get when you put a metric with a signature of (-+++) or (+---) into the Einstein Field Equations and then look at the local isometries induced on the tangent spaces and find the O(3,1) group. Local or not, isometries preserve curvature and Minkowski space has zero curvature.