Gravito-electromagnetic analogies

TL;DR

This paper reviews and extends various gravito-electromagnetic analogies, clarifying their connections, and explores their physical implications, including conditions for similarity and insights into gravitational radiation.

Contribution

It systematically reformulates and generalizes key GEM analogies, including exact formulations and new insights into gravitational radiation and the conditions for gravity-electromagnetism similarity.

Findings

Exact formulations of GEM analogies are developed.

The linearized gravity-electromagnetism analogy is derived as a limit.

Conditions for gravity-electromagnetism similarity are identified.

Abstract

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.