An intrinsic characterization of the Kerr metric

TL;DR

This paper establishes precise local conditions involving Riemann tensor invariants that uniquely characterize the Kerr metric among solutions of Einstein's equations.

Contribution

It provides necessary and sufficient conditions based solely on Riemann tensor concomitants to identify the Kerr metric.

Findings

Conditions are explicit and involve Riemann tensor concomitants.

The characterization is both necessary and sufficient.

Applicable to local metric analysis in general relativity.

Abstract

We give the necessary and sufficient (local) conditions for a metric tensor to be the Kerr solution. These conditions exclusively involve explicit concomitants of the Riemann tensor.