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Changing Electric Field causes Magnetic filed and changing Magnetic Field causes Electric Field. Is there anything similar in relation to Gravitational Field? What sort of field is created by varying Gravitational Field?

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In elektromagnetism there are intrinsic reasons that cause one field to generate the other. Yet, as far as I know, there's no symmetry in gravity that implies another field to be generated. –  romeovs Jun 14 '11 at 21:20
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The general answer is yes. The buzzword for this is "gravitomagnetism." –  Ted Bunn Jun 14 '11 at 22:10
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@Ted: well, there's no need to reduce to linear gravitomagnetic theory (if that's what you mean). A more proper answer is that there is no magnetic and electric field, there is just EM field and change in EM field produces change in EM field. Similarly, change in gravitational field produces change in gravitational field. Hopefully these statements sound trivial but that's the whole story, really :) –  Marek Jun 15 '11 at 11:06
    
In case it's not clear, I certainly agree with Marek on the physics. I think we're just choosing to emphasize different things. –  Ted Bunn Jun 15 '11 at 15:28
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You might want to look into gravitational waves. –  QEntanglement Jun 20 '11 at 10:11
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The only way this would work is to have a set of equations describing gravitation that are structurally the same as Maxwell's equations. Then you can have something similar to the concept of induction and induced fields. Ted Bunn above has pointed out already that gravitomagnetism is the name for this setup. Check out the wikipedia page on this:

http://en.wikipedia.org/wiki/Gravitomagnetism

It has a nice summary of the GEM equations and puts them right up next to Maxwell's equations so you can see the equivalences.

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It's useful to point out that the GEM equations are actually the result of Einstein's equations, so they really are a part of our currently accepted theory of gravity -- General Relativity. –  Mike Mar 6 '12 at 17:48
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The answer is very much yes! In fact, Gravity Probe B detected frame dragging effects by comparing rotation speed of four extremely precise gyroscopes onboard. As one might think, the force is very small for an object like earth rotating so slowly. However for fast rotating massive bodies, is has noticeable effects. Supermassive black holes in active nuclei have enormous jets that are very closely aligned even at megaparsec (millions of light years) distances. As far as the nature of the field created, it is very much congruent to the relationship between the electric field and the magnetic field.

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Isn't frame dragging an example of this?

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This does not provide an answer to the question. To critique or request clarification from an author, leave a comment below their post. –  Manishearth Nov 24 '12 at 13:24
    
It is actually a proposed answer. It just happened to be (for rhetorical purposes) formulated as a "question". –  Florin Andrei Nov 29 '12 at 17:58
    
I am not referring to that. Here on Physics.SE we expect answers to have conceptual explanation--one line answers are highly discouraged. Such "one liners" can be classified as comments, not actual answers. –  Manishearth Nov 29 '12 at 20:26
    
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. –  Emilio Pisanty Dec 10 '12 at 19:44
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