Gravitomagnetism refers to a set of formal analogies

Analogy

Analogy is a cognitive process of transferring information or meaning from a particular subject to another particular subject , and a linguistic expression corresponding to such a process...

 between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations

Einstein field equations

The Einstein field equations or Einstein's equations are a set of ten equations in Albert Einstein's general theory of relativity which describe the fundamental interaction of gravitation as a result of spacetime being curved by matter and energy...

 for general relativity

General relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

. The most common version of GEM is valid only far from isolated sources, and for slowly moving test particles. The equations were first published in 1893, before general relativity, by Oliver Heaviside

Oliver Heaviside

Oliver Heaviside was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations , reformulated Maxwell's field equations in terms of electric and...

 as a separate theory expanding Newton's law.



This approximate reformulation of gravitation

Gravitation

Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...

 as described by general relativity

General relativity

General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

 makes an apparent force appear in a frame of reference

Frame of reference

A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer.It may also refer to both an...

 different from a freely moving, gravitating body.