Revisiting the rotating Bertotti-Robinson electromagnetic universe

Abstract

We introduce an exact solution of Einstein-Maxwell equations of general relativity which represents a uniform electromagnetic field in the rotating state. This solution generalizes the Bertotti-Robinson electromagnetic universe. The paper can be devoted into two parts. In the first part we introduce the rotating Bertotti-Robinson electromagnetic universe solution with its major properties. In the second part we investigate the geodesics in that solution. Namely we discussed the particle geodesics confined to the azimuthal plane theta = pi/2 and we have obtained the exact first integral of the geodesics equation. For a detailed analysis we choose a special rotational parameter (alpha(2) = 1/3) and we show that the path of charged and uncharged particles both spiral and move along a cylindrical surface toward a focal point. Hyperbolicity and rotation characterize the unidirectional flow of particles in such a universe.