Einstein field equation, assuming a weak gravitational field or reasonably flat spacetime, are analog to Maxwell's equations for electromagnetism.
In the framework of the generalized Clifford algebra, it can be proved that gravitation and electromagnetism are the same field. In nature also gravitation and electromagnetism are strongly connected: in strong gravitational fields of planets there is necessarily an electromagnetic field of a planet. Also in strong deformations, for example, in earthquakes, in volcanic eruptions, electromagnetic glow, lightning, etc. are necessarily present. Perhaps sonoluminescence is also the result of gravi-electromagnetism. But how to prove it?
Read this article
Krylov, S. M. Vortical gravitational fields of natural and manmade origin and their wave properties / S. M. Krylov, G. A. Sobolev // Volcanology & Seismology. – 1999. – Vol. 20, No. 3. – P. 343-360.
Sergio Perez Felipe
If you haven't done so already, I recommend you take a look at "Gravitation and Cogravitation" by Oleg D. Jefimenko (ISBN 0-917406-15-X - paperback). This contains derivations of the Maxwell-like equations for (weak) gravitational fields and discusses examples. I myself have been able to derive the correct result for the perihelion precession of Mercury using these gravitoelectromagnetic equations despite the fact that Jefimenko obtained the wrong value in his book (!).
Thank you so much! I will definitely read the books (articles) you recommend. I think they will help me understand the nature of gravitoelectromagnetism more deeply.
There are also articles (mine) on the unification of gravity and electromagnetism in English and Russian. In these articles, gravity and electromagnetism are combined in a slightly different way, i.e. in generalized Clifford algebra and without Lagrangian formalism. How right I am is for the readers - the experts - to judge.
This is not self-promotion, but if you are interested:
https://www.researchgate.net/publication/374625568_Clifford's_algebra_as_a_universal_mathematical_tool_for_describing_and_unifying_gravity_and_electromagnetism
https://sci-article.ru/number/03_2017.pdf pp. 10-15
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