I think of gravitomagnetism as as the "magnetic" portion of gravity, with gravity being the "electric" portion. Since gravity ("electric") seems to affect space (which the LIGO could detect) what does the gravitomagnetic portion affect? Was it not detected or did the LIGO respond to both components?
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3While you may think of things that way, I don't believe that the framework for GR does, so you probably need to clarify how what you are asking corresponds to GR. – Jon Custer Mar 08 '16 at 21:05
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"This apparent field may be described by two components that act respectively like the electric and magnetic fields of electromagnetism, and by analogy these are called the gravitoelectric and gravitomagnetic fields, since these arise in the same way around a mass that a moving electric charge is the source of electric and magnetic fields. " – Jiminion Mar 08 '16 at 21:16
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Related: http://physics.stackexchange.com/q/75006/2451 and links therein. – Qmechanic Mar 08 '16 at 21:17
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Gravity is not the "electric" portion. Gravitoelectromagnetism describes the effect of the weak gravitational field in terms of two vector fields, whose equations of motion happen to show some formal analogy to those of the EM field. So assigning physical significance to the separation of the "electrical" and "magnetic" components of the field is even more futile that in the EM case. The comments under http://physics.stackexchange.com/q/75006/2451 discuss that you get wrong results for gravity waves, when applying gravitoelectromagnetism naively. – Sebastian Riese Mar 16 '16 at 14:08