  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.
