Gravitomagnetism: Derivation, Theory & Insights - Bill

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In summary, the conversation discusses the author's interest in deriving Maxwell's equations from Coulomb's Law and Special Relativity, and their application to gravity. The author also mentions a book they purchased on the topic and asks if there is literature on the gravitomagnetic theory being a limiting case of General Relativity. The response highlights a paper that may be of interest and also mentions a thread on gravitomagnetism and a book by Feynman on gravitation.
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I often post a derivation of Maxwell's equations from Coulomb's Law and SR:
http://cse.secs.oakland.edu/haskell/Special Relativity and Maxwells Equations.pdf

The author has also published book about it, I sort of on a whim purchased:
https://www.amazon.com/dp/1516864743/?tag=pfamazon01-20

In it he also applied the same derivation to gravity, and not surprisingly ends up with the Gravitomagnetic equations. They are, unlike Maxwell's equations, not relativistically invariant, nor do they take into account gravity gravitates that Peter Donis wrote excellent insight articles about:
https://www.physicsforums.com/insights/does-gravity-gravitate/

It must fail because unlike electric charge mass 'charges' are not invariant as it forms part of the stress energy tensor.

My query is does anyone know any literature about the gravitomagnetic theory being some kind f limiting case of GR, like linearised gravity is?

Thanks
Bill
 
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bhobba said:
They are, unlike Maxwell's equations, not relativistically invariant

Yes, that's because the source, unlike in the Maxwell case, is not a 4-vector, but a tensor.

bhobba said:
does anyone know any literature about the gravitomagnetic theory being some kind f limiting case of GR, like linearised gravity is?

Section 1.2 of this paper might be the sort of thing you are looking for:

https://arxiv.org/pdf/gr-qc/0311030.pdf
 
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bhobba said:
I often post a derivation of Maxwell's equations from Coulomb's Law and SR:
http://cse.secs.oakland.edu/haskell/Special Relativity and Maxwells Equations.pdf
Hmm... Haskell appears to use a Loedel-type diagram and analysis, which works for special cases... but is limited, compared to a Minkowski diagram and its methods.

On gravitomagnetism,
this ancient thread (my post and the rest of thread) might be of interest.
https://www.physicsforums.com/threads/there-is-no-gravitational-dipole.80710/#post-691492
https://www.physicsforums.com/threads/gravitomagnetism-and-gr.54932/
 
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It's not about gravitomagnetism, but as usual Feynman is a very good read to get an alternative view on fundamental physics:

R. P. Feynman, Feynman lectures on gravitation,
Addison-Wesley, Reading, Massachusetts (1996).
 
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1. What is gravitomagnetism?

Gravitomagnetism is a theory in physics that describes the gravitational effects of a moving mass on other masses. It is similar to how a moving electric charge creates a magnetic field, but instead, it involves the effects of a moving mass on the curvature of spacetime.

2. How is gravitomagnetism derived?

Gravitomagnetism is derived from Einstein's theory of general relativity. It is based on the concept that mass and energy can curve spacetime, and a moving mass will create a "gravitomagnetic" field that affects other masses.

3. What are the main insights of gravitomagnetism?

One of the main insights of gravitomagnetism is that it allows for the prediction and explanation of phenomena such as frame-dragging, which is the dragging of spacetime caused by the rotation of a massive object. It also helps to explain how objects in orbit around a rotating body experience gravitational forces.

4. How does gravitomagnetism differ from Newton's law of gravitation?

Gravitomagnetism differs from Newton's law of gravitation in that it takes into account the effects of a moving mass on the curvature of spacetime, whereas Newton's law only considers the direct gravitational force between two masses. Gravitomagnetism also applies to objects moving at high speeds, while Newton's law is only accurate for slower-moving objects.

5. Has gravitomagnetism been proven experimentally?

While gravitomagnetism has not been directly proven experimentally, there is evidence that supports its existence. For example, the frame-dragging effect has been observed in the orbits of satellites around Earth, and the Lense-Thirring effect, which is the precession of the orbit of a gyroscope around a rotating mass, has also been observed. However, more research and experiments are needed to fully confirm the theory of gravitomagnetism.

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