Black Holes have Intrinsic Scalar Curvature

Abstract

The scalar curvature [Formula: see text] is invariant under isometric symmetries (distance invariance) associated with metric spaces. Gravitational Riemannian manifolds are metric spaces. For Minkowski Space, the distance invariant is [Formula: see text], where [Formula: see text], [Formula: see text] are arbitrary 4-vectors. Thus the isometry symmetry associated with Minkowski Space is the Poincaré Group. The Standard Model Lagrangian density [Formula: see text] is also invariant under the Poincaré Group, so for Minkowski Space, the scalar curvature and the Standard Model Lagrangian density are proportional to each other. We show that this proportionality extends to general gravitational Riemannian manifolds, not just for Minkowski Space. This predicts that Black Holes have non-zero scalar curvatures [Formula: see text]. For Schwarzschild Black Holes, [Formula: see text] is predicted to be [Formula: see text], where [Formula: see text] is the Schwarzschild radius. The existence of [Formula: see text] means that Black Holes cannot evaporate.