Stationary and static cylindrically symmetric Einstein spaces of the Lewis form

The derivation of the general solutions for stationary and static cylindrically symmetric Einstein spaces of Lewis form is revisited and the physical and geometrical meanings of the parameters appearing in the resulting solutions are discussed. We find 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.