(adsbygoogle = window.adsbygoogle || []).push({}); gravitomagnetism equations--wikipedia wrong?

Hi, I read the wikipedia article from:

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

(scroll down to the "Maxwell's eq" for gravity)

where it says

[tex]\nabla \times \mathbf{B}=-4\pi G\mathbf{J}[/tex]

(neglect the other terms)

however, when I compare that to Sean Carroll's book of GR (spacetime and geometry),

on page 282, (7.31) it reads something like

[tex] \nabla^2 \mathbf{\omega}=-16 \pi G T_{0j}=-16 \pi G \mathbf{J}[/tex]

Carroll defines,

[tex]\mathbf{B}=\nabla \times \mathbf{\omega}[/tex]

so in effect, we have something like

[tex] \nabla \times \mathbf{B}=-16 \pi G \mathbf{J}[/tex]

while a factor of two is reasonable since the the force law in Carroll's book is without the 2 in front of B, the additional factor of 4 is just weird... I could not get around that at all. Is wikipedia wrong or am I missing something?

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# Gravitomagnetism equations-wikipedia wrong?

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