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As I learn, the gravity is caused by the spacetime curvature. Is there any gravitational/magnetic field that really exists around the Earth, or any other planets?

Since the planets/stars rotate, does this cause the space time curvature to twist in the direction of their rotation? If it does then the gravitational pull should also twist the the path of the objects falling(though we may not perceive the curvature of this path, we should be able to calculate at-least theoretically)

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Unlike gravitation, which is entirely a result of space-time curvature, magnetic fields do exist and there is a magnetic field around the Earth and many other planets.

(There is a deeper level of understanding of electromagnetism called Quantum Electrodynamics which explains how fields work in terms of more fundamental concepts, but unlike gravity, the E-M field does exist. (And there is hope -- so far unrealized -- that eventually all of the fields of nature plus gravity will be explained as aspects of one yet deeper thing. But not today.))

Frame dragging -- the distortion of space-time by a rotating body -- does exist and the link suggested by @PM (en.wikipedia.org/wiki/Frame-dragging) is a good place to start. Frame dragging has been measured by careful observation of satellite orbits, and possibly by astronomical observations. The Gravity Probe B satellite measure a closely related effect. As far as I know, the effect is too small to have been measured in the lab.

Frame dragging does indeed affect the path of a falling body, though for the Earth the effect is really, really small. It would be large near a millisecond pulsar or a rapidly rotating black hole. It's also large for merging black holes and is an essential part of the calculations of the gravitational waves emitted during the final rotations before merger.

The effect can be precisely calculated and agrees perfectly with the (still rather crude, alas!) experiments and observations.

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  • $\begingroup$ Hi @Mark Olson Thanks for the insight. I have one more query, If there is a magnetic field, does it interfere with the space. Since space is curved, does this cause a curvature in the magnetic field. Does this magnetic field has any effect on the gravity that is caused due to space time curvature? Sorry for too many questions at once :)) $\endgroup$ – Aditya Y Oct 3 '18 at 7:49
  • $\begingroup$ To a very good approximation, you can think of a magnetic field as existing in the curved spacetime. So, yes, the magnetic field curves with spacetime. But the physical size of spacetime curvature is very, very small except near neutron stars and black holes, so the effect is probably not measurable. Spacetime is curved by the presence of mass-energy, so if the magnetic field has energy, it curves spacetime. But this effect is even more infinitesimal for any magnetic field we have access to. I doubt it's measurable. $\endgroup$ – Mark Olson Oct 3 '18 at 17:50
  • $\begingroup$ Got it @Mark Olson. The gravity on earth is measured to be 9.8 m/s/s. Does this mean the space time curvature is pushing the bodies with this acceleration? $\endgroup$ – Aditya Y Oct 8 '18 at 6:07
  • $\begingroup$ Wow. That's a very hard question to answer briefly, clearly, and without mathematics. I honestly don't know how to go much beyond saying that near Earth's mass warps spacetime near it so that a freely falling body accelerates at 9.8 m/s/s. (I realize that doesn't do much more than restate your question. Sorry!) $\endgroup$ – Mark Olson Oct 8 '18 at 12:51

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