On the Lewis metric (Q2738268)

A natural classification of stationary cylindrically symmetric vacuum solutions (Weyl and Lewis) of Einstein's equations is found which enables better understanding of the role of parameters entering the metric functions. NEWLINENEWLINENEWLINEThe field equations for the metric potentials in a new parametrization describe a motion of a classical particle in a central force field. The solution then corresponds to a conic intersection of a plane and a hyperbolic paraboloid surface. When the conic is a hyperbola or ellipse the solution belongs to the Weyl and Lewis class, respectively, both being of the Petrov type I. The solution where the conic is two straight lines is of the Petrov type II and was formerly considered as a limit of the previous two solutions.