Kantowski–Sachs metrics with source: A conformally invariant scalar field

Abstract

Solutions of the coupled Einstein conformally invariant massless scalar field equations are derived under the assumption that the metric admits a four-parameter group of isometries with spacelike generators, where further, the three-parameter subgroup of isometries acts multiply transitive on two-dimensional surfaces. The general solution of the system is obtained and some properties concerning the singularity structure are briefly discussed. Results for all three cases are presented, i.e., for the case where the three-dimensional group of isometries acts on two-dimensional orbits of positive, negative, or zero curvature. The first two classes belong to the Kantowski–Sachs class of metrics, while the third one is of Bianchi type I with additional rotational symmetry.