A locally conformally symplectic structure on Kerr space-time

TL;DR

This paper explores a new geometric structure called a locally conformally symplectic structure on Kerr space-time, linking it to integrable systems and cobordism categories in differential geometry.

Contribution

It introduces a novel interpretation of Kerr space-time's geodesic system via locally conformally symplectic structures and defines related cobordism categories.

Findings

Identification of a locally conformally symplectic structure on Kerr space-time

Connection between integrable geodesic systems and symplectic geometry

Development of a cobordism category for contact 3-manifolds

Abstract

R Kerr's Ricci-flat Lorentz 4-manifold was shown by B Carter in 1968 to support a classically completely integrable system of geodesics; here we interpret this system in terms of a locally conformally symplectic structure, which we identify (\S 2.2) using characteristic classes defined by Kerr-Schild Cartesian coordinates (regarded as a map to the Cayley-Penrose compactification of Minkowski space). This leads to the definition of an interesting cobordism category of contact 3-manifolds and 4-dimensional locally conformally symplectic cobordisms between them.