For 10 points, name this concept from relativistic physics, a generalization of the Euclidean dot product, an infinitesimal measure of distance on a manifold.
The Reissner-Nordstrom version accounts for charge but not rotation. The magnitude of its determinant is a component in the natural volume form on the underlying space. The isometry group of a manifold preserves it. Its namesake connection preserves it under parallel transport. Multiplication by it or its inverse combined with a contraction will raise or lower an index of the multiplicand. If its quadratic forms in the associated vector space at each point has the same signature, then it (and the manifold it acts on) is pseudo- Riemannian. It has only diagonal elements in flat space. For 10 points, name this concept from relativistic physics, a generalization of the Euclidean dot product, an infinitesimal measure of distance on a manifold.
The Reissner-Nordstrom version accounts for charge but not rotation.
metric tensor