Gravito-electromagnetic analogies

We reexamine and further develop different gravito-electromagnetic (GEM) analogies found in the literature, and clarify the connection between them. Special emphasis is placed in two exact physical analogies: the analogy based on inertial fields from the so-called "1+3 formalism", and the analogy based on tidal tensors. Both are reformulated, extended and generalized. We write in both formalisms the Maxwell and the full exact Einstein field equations with sources, plus the algebraic Bianchi identities, which are cast as the source-free equations for the gravitational field. New results within each approach are unveiled. The well known analogy between linearized gravity and electromagnetism in Lorentz frames is obtained as a limiting case of the exact ones. The formal analogies between the Maxwell and Weyl tensors are also discussed, and, together with insight from the other approaches, used to physically interpret gravitational radiation. The precise conditions under which a similarity between gravity and electromagnetism occurs are discussed, and we conclude by summarizing the main outcome of each approach.Comment: 60 pages, 2 figures. Improved version (compared to v2) with some re-write, notation improvements and a new figure that match the published version; expanded compared to the published version to include Secs. 2.3 and

A non-static Einstein-Maxwell solution

The Einstein-Maxwell field equations are solved completely when the line element has the form (Equation presented) where h, A and B are functions of t only, and is thus non-static. The metric admits a four-parameter group of motions. The Weyl tensor is type D and the electromagnetic field is non-null