# Gravito-Electro-Magnetism problem

• JustinLevy
Yes, this is essentially the approach used in Maxwell's equations. However, I believe there is a problem with this approach as well. Maxwell's equations only work for situations where the electric and magnetic fields are perpendicular to each other. In the gravitoelectromagnetic equivalent, the electric field is not perpendicular to the magnetic field, so this approach won't work. In summary, the Wikipedia article on gravitomagnetism has a sign error which leads to a run-away solution.f

#### JustinLevy

Hello,
There is either a mistake on Wikipedia (http://en.wikipedia.org/wiki/Gravitomagnetic), or I am making some really stupid mistakes (more likely). Any help in finding my error would be appreciated.

First let's look at a simple electromagnetism problem. Consider a charged ring at rest. Now apply a magnetic field. The change in magnetic flux will cause the ring to start spinning, creating a magnetic field to reduce the enclosed flux.

Now look at the gravitoelectromagnetic equivalent. Consider a ring with a non-zero mass at rest. Now apply a gravitomagnetic field. The change in flux will cause the ring to start spining, BUT due to the different signs (in GEM as compared to Maxwell's eqs.), this will INCREASE the enclosed flux. And thus will create a run away solution.

Is there a sign error on Wikipedia? Am I making a sign error? Or is there some reason that this simple thought experiment falls outside the "applicability regime" of this approximation? (If so, why? There aren't fast moving masses, nor is this a "strong field" problem.)

Doh. I found my error.

Due to the sign change for the "electric"-field source equation the ring will indeed spin in the opposite direction. But there is also a corresponding change in the sign of the "magnetic"-field source equation (ie you use a "left hand rule" for mass current / magnetic fields). And thus the magnetic flux is indeed reduced not increased.

Considering the stupidity of that mistake, maybe I should just stop and get some sleep, but I can't figure out a related thought experiment:

Intial configuration:
one ring with a mass is spinning
there is another ring with a mass oriented perpendicularly to the first and is not spinning.

Now, rotate the non-spinning ring to be parallel with the first. The enclosed magnetic flux changes, and the ring will start spinning. But this decreases the flux in the first ring, so it will start spinning faster ... creating more flux in the second ring ... etc. Again I have somehow made a mistake which leads to a run away solution.

I assume it is another stupid mistake. I really need sleep, I'll work on it more later. Good night.

at an earlier time Chris Hillman (who shows up here) suggested that the article be renamed "Gravitoelectromagnetism" instead of "Gravitomagnetism". i was just waiting for a physicist (well Chris is a mathematician, but he is also a physicist by my reckoning) to say so, and i changed it which started off an edit war with a now banned editor named "Nixer".

anyway, what do you guys think? what should the article be primarily named (with the other name redirecting to it)?

anyway, what do you guys think? what should the article be primarily named (with the other name redirecting to it)?
This really isn't my field (as is obvious from above) so I can't help with "preferred semantics" questions. Sorry.

On further inspection I realized that the equivalent electromagnetic situation also seems to have the same problems as mentioned above. I also noticed that in the discussion above I am considering all contributions except the partial E / partial t term in the magnetic field source equation. So unless I am overlooking another error, it appears the displacement current term is the only thing left to save us from the run-away solution.

But can't I just state that the ring will be turned away from the perpendicular orientation (to make the mutual inductance non-zero) arbitrarily slow so that the displacement current term can be ignored?