Gravitomagnetism was created to account for the rotational motion of the celestial object by modifying general relativity in the spirit of Maxwell's equation. I wonder if the inventor(s) of gravitomagnetism have ever wondered if their theory may violate the equivalence principle that Einstein used to formulate his original theory of general relativity.
First of all, rotational motion is described by general relativity, so there's no need to modify it for that reason.
The only way additional fields (beyond the metric) that describe the gravitational interaction, can lead to violations of the equivalence principle is if they can't be eliminated, by redefinition, from the gravitational part of the Einstein-Hilbert action and their contribution can't be described just by their energy-momentum tensor.
In supergravity there does exist a vector field-now called the graviphoton, but it doesn't have anything to do with electromagnetism-that can't be eliminated and can describe deviations from the equivalence principle, cf. Article Antigravity: A crazy idea?
by mediating a repulsive interaction (that's why in the paper linked to it's called the ``antigraviton'').
The simple answer is: gravitomagnetism is part of the General Theory of Relativity, so no modifications to GRT have been made whatsoever. The reason why the term "gravitomagnetism" is used is because the Einstein equations, being 4-tensor equations, contain a part that have a certain structural similarity to the "magnetic" part of Maxwell's equations for electrodynamics, that's all. (There is a connection between spacetime curvature and energy-momentum currents, not only sources.)
A simple example of a "gravitomagnetic" effect is the Lense-Thirring effect, or frame-dragging.
Ergo: the equivalence principle is of course not violated.
The gauge symmetry of Einstein's equations is the symmetry under local translations, the gauge symmetry of Maxwell's equations is the symmetry under local U(1) transformations. Totally different structures that lead to totally different properties, for mathematics as well as for physics.
The equivalence principle doesn't make sense within the framework known as ``gravimagnetism'', so it doesn't make sense to ask about how it could be violated.
The equivalence principle states that matter couples to the spacetime metric only through its energy-momentum tensor and that only the spacetime metric describes spacetime geometry. Gravimagnetism doesn't have anything to do with either statement.
Dear Prof,
Please to read my theoretical and mathematical proof of the universality of free fall, the equivalence principle, and the confirmation of the Einstein's theory of general relativity.
Please to give me your comment.
Best regards
Pr. Abdelouahed Tounsi ([email protected])
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