# Gravitomagnetism & Gravitational Waves

• Marin
What you're trying to do is compare a weak field limit E&M result with a full GR result. In summary, the article discusses the formal analogies between Maxwell's field equations and an approximation of the Einstein field equations for general relativity known as Gravitomagnetism. However, this approximation does not apply to gravitational waves, as they arise from a different equation and are not observed in this limit.

#### Marin

Hi all!

I was browsing Wikipedia when I came upon the following article:

http://en.wikipedia.org/wiki/Gravitomagnetism

It seems here they state a form of the complete linearized Einstein equations that resembles very much (or is mathematically identical to that of) Maxwell's equations, which are clearly linear.

However, it seems to me that this is inconsistent with the theory of gravitational waves, for the following reason:

It is a fact that from Maxwell's eqn's a wave eqn arises, EM waves being a consequence of accelerated charge. Mathematically /please, correct me, if I'm wrong/ it is the 1st time derivative of the dipole moment of the charge distribution that is responsible for the EM radiation, whereas it's power is proportional to the second time derivative of the charge distribution.

Unlike in EM, G waves arise from the 2nd time derivative of the transverse traceless part of the quadrupole moment of the energy/mass distribution. The power going like the 3rd derivative of it. So it turns out we need the rate of change of the acceleration for them.

Since the mathematics of gravitomagnetism seems pretty much the same as this of electromagnetism, I suspect the corresponding radiation has to also possesses the same mathematical characteristics which looks like a contradiction to the theory of G waves...

So, what do you think of it?

PS: I probably overlook something, since there are various papers listed in the references, but what is it?

"Gravitomagnetism ... refers to a set of formal analogies between Maxwell's field equations and an approximation, valid under certain conditions, to the Einstein field equations for general relativity."
GEM can be applied to the weak field limit of GR, and thus understandably doesn't apply to gravitational waves.

Ok, so suppose the gravitomagnetic eqn's, as stated in the article, are a valid approximation under some physical conditions, whatever they may be.

There's still a wave equation arising from them, which accounts for the description of radiation in this particular limit.

Clearly, it's not gravitational waves, so what can it be? Is it observed at all?

Marin said:
Ok, so suppose the gravitomagnetic eqn's, as stated in the article, are a valid approximation under some physical conditions, whatever they may be.

There's still a wave equation arising from them, which accounts for the description of radiation in this particular limit.

Clearly, it's not gravitational waves, so what can it be? Is it observed at all?

Wave equation, and "gravitational waves" are apples and oranges.