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In weak gravitaional fields, we can write equations analogous to the Maxwell equations: Gravitoelectromagnetism.

  1. Do the gravitoelectric field and the gravitomagnetic field transform like components of a second rank tensor (2-form, to be exact) analogous to the Faraday tensor?

If so,

  1. Does this tensor have some immediate relation to the Riemann/Ricci/Einstein tensors?

  2. Can we use it to write the Einstein-Hilbert action in Yang-Mills form in this approximation?

Rd Basha
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    Check this thesis on arxiv, you'll get your answers. Gravitoelectromagnetism: Basic principles, novel approaches and their application to Electromagnetism – Shaktyai Aug 14 '22 at 16:55
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    Related: https://physics.stackexchange.com/q/75006/2451 and links therein. – Qmechanic Aug 14 '22 at 17:07

1 Answers1

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  1. Yes, Gravitoelectromagnetism rank 2 tensor is like the electromagnetic tensor $F_{\mu\nu}$

  2. I'm not aware of any relation. The tensors you listed depend on 2nd derivatives of the gravitational potential $g_{\mu\nu}$ while the gravitoelectromagnetic tensor depends on 1st derivatives.

  3. Yes, you can use gravitoelectromagnetism to approximate gravity in qft. I don't think you should use the EH action rather the maxwell lagrangian for gravitoelectromagnetism.

Habouz
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