synch said:
Is there a gravitational analog of electromagnetic force?
[Apart from the obvious "static" forces, ie electrostatic between fixed charges and gravitational between fixed masses.]
I am thinking of the classic situation of a moving charge (or current) creating a magnetic field which then affects other moving charges. So a question by analogy, does a moving mass have an additional field which is only detected by other moving mass ? It would be very very small I guess.
There is a way to break down, or decompose, the curvature tensor in General relativity (called the Riemann tensor) into parts, which can be loosely interpreted as an "electric part", a "magnetic part", and a "topological (curvature) part". This is a bit different than the GEM formalism, also known as Gravitoelectromagnetism, which has also been mentioned in this thread, in that it works even in the strong field case, rather than being a linear approximation.
The first two parts would probably be described in popularizations as a 'force'. (That's not 100% accurate). The last part would be described in popularizations as "the curvature of space" rather than as a force. (That description is similarly not 100% accurate). I personally think it's close enough to not be horribly misleading, which is pretty good for a popularization about General Relativity.
The original paper is in French and I haven't been able to get a hold of it or a translation (or even the original). See the wiki article
https://en.wikipedia.org/wiki/Bel_decomposition for the Wiki reference. Unlike the GEM formalism, the decomposition works even in strong fields. There are some discussions in "Gravitation" which break the Riemann tensor into different parts, but they don't mention Bel by name.
To perform the decomposition, one needs to define what might be called "the observers flow of time", more formally a timelike congruence, or a unit timelike vector field. This additional information given by the flow of time gives the necessary information to sensibly decompose spacetime as a unified entiity into a spatial part and a time part, and similarly how to decompose the electromagnetic field into an "electric" part and a "magnetic" part.
Nasa's descritpion of Gravity Probe B disucssses the use of the GEM analogy in the context of the Gravity probe B experiment, though I find their presentation a bit murky. If you are not familiar, gravity probe B was designed to detect frame dragging effects predicted by GR, effects which are even smaller than the GEM effects, which are also present and also measured by the GPB experiment. To give an idea of the magnitude of the effects, it would take only about 200,000 years for the GPB gyroscopes to precess through a full 360 degree arc due to the geodetic effect.
