Stationary and static cylindrically symmetric Einstein spaces of the Lewis form

TL;DR

This paper revisits the solutions for stationary and static cylindrically symmetric Einstein spaces of Lewis form, clarifying the physical meaning of parameters and their relation to topology and gravitational fields.

Contribution

It provides a detailed analysis of the parameters in Lewis form solutions, highlighting their physical and topological significance, and clarifies the role of the cosmological constant.

Findings

Three parameters are essential for the solutions.

One parameter characterizes the local gravitational field.

Two parameters relate to topological identifications.

Abstract

The derivation of the general solutions for stationary and static cylindrically symmetric Einstein spaces of Lewis form is revisited and the physical and geometrical meaning of the parameters appearing in the resulting solutions are investigated. It is shown that three of the parameters (and the value of the cosmological constant) are essential, of which one characterizes the local gravitational field and appears in the Cartan scalars, while the remaining two give information about the topological identification made to produce cylindrical symmetry. Other than the cosmological constant, they can be related to the parameters of the vacuum Weyl and Lewis classes, whose interpretation was previously investigated by da Silva et al. (1995a, 1995b).