Mah. Maccallum et No. Santos, STATIONARY AND STATIC CYLINDRICALLY SYMMETRICAL EINSTEIN-SPACES OF THE LEWIS FORM, Classical and quantum gravity, 15(6), 1998, pp. 1627-1636
The derivation of the general solutions for stationary and static cyli
ndrically 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 parameter
s (and the value of the cosmological constant) are essential, of which
one characterizes the local gravitational field and appears in the Ca
rtan scalars, while the remaining two give information about the topol
ogical identification made to produce cylindrical symmetry. Other than
the cosmological constant, they can be related to the parameters of t
he vacuum Weyl and Lewis classes, whose interpretation was previously
investigated by da Silva et al.