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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?