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 geodesies confined to the azimuthal plane 0 = π/2 and we have obtained the exact first integral of the geodesics equation. For a detailed analysis we choose a special rotational parameter (a 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.
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