Spinning cylinders in general relativity: a canonical form for the Lewis metrics of the Weyl class

TL;DR

This paper introduces a new canonical form for the Lewis metrics of the Weyl class in general relativity, highlighting their physical features, limits, and differences from the Kerr spacetime.

Contribution

It presents a simplified, parameter-dependent canonical form for Weyl class metrics, clarifying their local staticity and physical interpretation.

Findings

The canonical form depends on three parameters: mass, angular momentum, and angle deficit.

It reveals the local static but non-global static nature of these spacetimes.

Contrasts with Kerr spacetime, illustrating differences in staticity and physical properties.

Abstract

In the main article [CQG 38 (2021) 055003], a new "canonical" form for the Lewis metrics of the Weyl class has been obtained, depending only on three parameters -- Komar mass and angular momentum per unit length, plus the angle deficit -- corresponding to a coordinate system fixed to the "distant stars" and an everywhere timelike Killing vector field. Such form evinces the local but non-global static character of the spacetime, and striking parallelisms with the electromagnetic analogue. We discuss here its generality, main physical features and important limits (the Levi-Civita static cylinder, and spinning cosmic strings). We contrast it on geometric and physical grounds with the Kerr spacetime -- as an example of a metric which is locally non-static.