IX.—The Gravitational Field of a Distribution of Particles Rotating about an Axis of Symmetry

Abstract

The generalisation to the stationary case of the solution given by Weyl (1918) of Einstein's gravitational equations in a statical axially symmetric universe, has been attempted by various writers. It has not, however, so far been possible to reduce the equations to linear form and thus to find the most general solution. A set of special solutions has been obtained by Lewis (1932), valid in a region free of matter, which contain Weyl's solution as a particular case. They depend upon an arbitrary solution of the equation