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We think that the electric field and gravitational field operate similarly with their corresponding charges/masses. With just a difference that the electric field is sometimes attractive and sometimes repulsive.

Now I have read that when a charged particle moves the electric field lines associated with it, it is distorted in one way because of the finite time required to get propagated, and this is the cause of the existence of the magnetic field (if calculus is used it can be proven mathematically).

So why is it not the same with the gravitational field? Why is there nothing like a Gravitational Magnetic Field?

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Can you provide a reference that really says that magnetic fields are caused by finite propagation and such? For me, electric and magnetic fields are just equal components of the electromagnetic field strength tensor, none is "the cause" of the other. Also, can you really write down what the "gravitational field" is? (That is also a point of contention between different approaches to a gauge view on GR) – ACuriousMind Jul 29 '14 at 17:22
    
Now I am not finding any source proving the points that you want to be proved...I had a confusion regarding the generation of magnetic field due to the motion of a charge...facebook.com/events/539159816188874 In context of this question I found the points that I have talked here... – Dvij Jul 29 '14 at 17:34
    
up vote 16 down vote accepted

There is a sort of analog called gravitomagnetism (or gravitoelectromagnetism), but it is not discussed that often because it applies only in a special case. It is an approximation of general relativity (i.e. the Einstein Field Equations) in the case where:

  • The weak field limit applies.
  • The correct reference frame is chosen (it's not entirely clear to me exactly what conditions the reference frame must fulfill).

In this special case, the equations of GR reduce to:

$$\nabla\cdot \vec{E}_g = -4\pi G \rho_g$$ $$\nabla\cdot \vec{B}_g = 0$$ $$\nabla\times \vec{E}_g = -\frac{\partial \vec{B}_g}{\partial t}$$ $$\nabla\times \vec{B}_g = 4\left(-\frac{4\pi G}{c^2}\vec{J}_g+\frac{1}{c^2}\frac{\partial \vec{E}_g}{\partial t}\right)$$

These are of course a close analogy to Maxwell's equations of electromagnetism.

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Can't we predict gravitational magnetism using classical mechanics only...( without using concepts of relaivity and spacetime ? ) – Dvij Jul 29 '14 at 17:44
    
@Dvij I don't think so... I can't think of any way in classical mechanics to get the angular momentum of one body (gravitational analogue of the dipole moment) to couple to the mass of another. – Kyle Oman Jul 29 '14 at 17:51
    
@Kyle: Try assuming the coupling is nonzero and crunch. I proved L of a photon is independent of wavelength using no QM or Rel assumptions that way. – Joshua Jul 29 '14 at 18:06
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@Dvij: you can't predict normal magnetism using classical mechanics only. To see that you need magnetism if you have an electrical force, you have to make an appeal to Lorentz invariance. – Jerry Schirmer Jul 29 '14 at 18:09
    
@Joshua hmmm, can you still call it classical mechanics in that case? – Kyle Oman Jul 29 '14 at 18:15

There is a gravitational analogue of the magnetic field. See gravitoelectromagnetism and frame dragging on Wikipedia.

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I don't know GR...Can you explain only significance without using terminology of GR ? – Dvij Jul 29 '14 at 17:41
    
@Dvij See the Wikipedia gravitoelectromagnetism article. Gravitoelectromagnetism is wholly analogous to Maxwell's equations together with an ever-so-slightly different Lorentz force law. GEM is a known weak field approximation to the Einstein field equations; it's really like Newtonian gravity with a time delay - so kind of a minimum effort to marry Newtonian gravity with the special relativistic ruling out of faster-than-light signalling. Note that GEM is not Lorentz-covariant (even though Maxwell's equations are), since there is no obvious way to make the source (mass and its current) ... – WetSavannaAnimal aka Rod Vance Jul 3 at 6:02
    
@Dvij .... into a four-vector, unless you use rest mass and its current (which would leave known gravitational effects unexplained). – WetSavannaAnimal aka Rod Vance Jul 3 at 6:03

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