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Gravitatomagnetic Analogs of Electric Transformers

Linearized general relativity admits a formulation in terms of gravitoelectric and gravitomagnetic fields that closely parallels the description of the electromagnetic field by Maxwell's equations. For steady mass currents, this formalism has been used to understand gravitomagnetic effects like the Lense-Thirring dragging of inertial frames. For time-varying mass-energy currents, the analog of Faraday's law suggests new effects based on the gravitational equivalent of a transformer where such currents take the place of electrical currents. New experimental possibilities are suggested including a novel coupling mechanism of electromagnetism to gravity, new tests of general relativity in the ultrarelativistic limit using particle beams in the LHC, and searches for a materials exhibiting the gravitational analog of ferromagnetism.