On the parameters of Lewis metric for the Lewis class

TL;DR

This paper investigates the physical and geometric significance of the four parameters in the Lewis metric for the Lewis class, relating them to vorticity and analyzing their properties through junction conditions and Cartan scalars.

Contribution

It clarifies the meaning of Lewis class parameters, their relation to vorticity, and their geometric properties, including their distinction from Minkowski and Levi-Civita spacetimes.

Findings

Parameters relate to vorticity of the source.

Lewis class cannot reduce to Minkowski spacetime.

Parameter for vorticity appears explicitly in Cartan scalars.

Abstract

The physical and geometrical meaning of the four parameters of Lewis metric for the Lewis class are investigated. Matching this spacetime to a completely anisotropic, rigidly rotating, fluid cylinder, we obtain from the junction conditions that the four parameters are related to the vorticity of the source. Furthermore it is shown that one of the parameters must vanish if one wishes to reduce the Lewis class to a locally static spacetime. Using the Cartan scalars it is shown that the Lewis class does not include globally Minkowski as special class, and that it is not locally equivalent to the Levi-Civita metric. Also it is shown that, in contrast with the Weyl class, the parameter responsible for the vorticity appears explicitly in the expression for the Cartan scalars. Finally, to enhance our understanding of the Lewis class, we analyse the van Stockum metric.