An intrinsic characterization of spherically symmetric spacetimes

TL;DR

This paper establishes explicit tensor-based criteria to identify spherically symmetric spacetimes, enabling precise classification of solutions like Schwarzschild and Reissner-Nordström within general relativity.

Contribution

It provides necessary and sufficient local conditions involving Riemann tensor concomitants for classifying spherically symmetric solutions, including non conformally flat cases.

Findings

Derived explicit conditions for spherically symmetric metrics

Applied criteria to classify Schwarzschild, Reissner-Nordström, and Lemaître-Tolman-Bondi solutions

Enhanced understanding of spacetime symmetry characterization

Abstract

We give the necessary and sufficient (local) conditions for a metric tensor to be a non conformally flat spherically symmetric solution. These conditions exclusively involve explicit concomitants of the Riemann tensor. As a direct application we obtain the {\em ideal} labeling of the Schwarzschild, Reissner-Nordstr\"om and Lema\^itre-Tolman-Bondi solutions.