On the parameters of Lewis metric for the Weyl class

TL;DR

This paper interprets the four parameters of the Lewis metric within the Weyl class, linking them to physical properties like vorticity and energy, and explores their geometric and physical implications.

Contribution

It provides a physical interpretation of the Lewis metric parameters, relating them to vorticity, energy, and gravitational analogs, and establishes local equivalence with Levi-Civita metrics.

Findings

One parameter is proportional to the vorticity of the source.

Another parameter relates to energy per unit length.

The Weyl class metric is locally equivalent to the Levi-Civita metric.

Abstract

We provide physical interpretation for the four parameters of the stationary Lewis metric restricted to the Weyl class. Matching this spacetime to a completely anisotropic, rigidly rotating, fluid cilinder, we obtain from the junction conditions that one of these parameters is proportional to the vorticity of the source. From the Newtonian approximation a second parameter is found to be proportional to the energy per unit of length. The remaining two parameters may be associated to a gravitational analog of the Aharanov-Bohm effect. We prove, using the Cartan scalars, that the Weyl class metric and static Levi-Civita metric are locally equivalent, i.e., indistinguishable in terms of its curvature.