An intrinsic characterization of spherically symmetric spacetimes

Abstract

We give the necessary and sufficient (local) conditions for a metric tensor to be a nonconformally flat spherically symmetric solution. These conditions exclusively involve explicit concomitants of the Riemann tensor. As a direct application we obtain the ideal labeling of the Schwarzschild, Reissner–Nordström and Lemaître–Tolman–Bondi solutions.