Invariants of the Kerr Vacuum

TL;DR

This paper investigates the invariants of the Kerr vacuum spacetime to clarify the nature of its ring singularity, emphasizing the importance of examining multiple invariants to avoid misinterpretation.

Contribution

It identifies two independent invariants of the Kerr vacuum derived from the Riemann tensor, highlighting the necessity of analyzing both to understand the singularity.

Findings

Both invariants must be examined to correctly interpret the singularity.

The invariants show the singularity is not directional when properly analyzed.

The study clarifies misconceptions about the Kerr ring singularity.

Abstract

The Kerr vacuum has two independent invariants derivable from the Riemann tensor without differentiation. Both of these invariants must be examined in order to avoid an erroneous conclusion that the ring singularity of this spacetime is "directional".