Analogies between Maxwell's and Einstein's field equations
This article is about the gravitational analog of electromagnetism as a whole. For the specific gravitational analog of magnetism, see frame-dragging.
Diagram regarding the confirmation of gravitomagnetism by Gravity Probe B
Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity. Gravitomagnetism is a widely used term referring specifically to the kinetic effects of gravity, in analogy to the magnetic effects of moving electric charge.[1] The most common version of GEM is valid only far from isolated sources, and for slowly moving test particles.
The analogy and equations differing only by some small factors were first published in 1893, before general relativity, by Oliver Heaviside as a separate theory expanding Newton's law.[2][better source needed]
^David Delphenich (2015). "Pre-metric electromagnetism as a path to unification". Unified Field Mechanics: Natural Science Beyond the Veil of Spacetime, Morgan State University, USA, 16–19 November 2014: 215–220. arXiv:1512.05183. doi:10.1142/9789814719063_0023. ISBN 978-981-4719-05-6. S2CID 118596433.
^O. Heaviside (1893). Electromagnetic Theory: A Gravitational and Electromagnetic Analogy. Vol. 1. The Electrician. pp. 455–464.
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