Electromagnetic Fields in a Homogeneous, Nonisotropic Universe

Abstract

A solution of the Einstein-Maxwell equations is derived which represents a closed universe of topology ${S}^{3}\ifmmode\times\else\texttimes\fi{}R$, filled with gravitational and electromagnetic radiation. We confine attention to the lowest of the large number of possible modes of radiation in such a universe. This mode has maximum symmetry consistent with the existence of a vector field; the universe is homogeneous but not isotropic, and is therefore a generalization of one of the solutions discussed by Taub. It is possible to solve explicitly for the metric coefficients. Some of the physical properties of the solution are discussed.