A gravitational magnetic field exists in general relativity
General relativity predicts the existence of a gravitomagnetic field, often studied under the weak-field approximation where mass currents produce effects analogous to magnetism (such as frame-dragging).
The claim that a gravitational magnetic field (gravitomagnetism) exists in general relativity is a well-established theoretical consequence of the weak-field or linearized approximation of Einstein's field equations. Papers [0], [3], and [4] explicitly discuss gravitoelectromagnetism, Maxwell-type gravitational equations, and frame-dragging effects, thereby directly supporting the claim.
Papini G. Some Classical and Quantum Aspects of Gravitoelectromagnetism.. 2020. https://doi.org/10.3390/e22101089
Discusses gravitoelectromagnetism, showing that in linear gravity, gravity can be carried by terms satisfying Maxwell-type equations analogous to a magnetic field.
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Mashhoon B. Gravitomagnetic Stern-Gerlach Force.. 2021. https://doi.org/10.3390/e23040445
Examines the gravitomagnetic Stern-Gerlach force within the framework of linearized general relativity.
Steven Carlip. The weak field approximation. 2019. https://doi.org/10.1093/oso/9780198822158.003.0008
Explains that the weak-field approximation of general relativity yields gravitoelectromagnetic and frame-dragging effects analogous to magnetic fields.
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