Jonathan Scott
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Linear frame dragging is the effect predicted by General Relativity that if a gravitational source is accelerated, this produces a small gravitational induction effect on other objects which tends to accelerate them in the direction of the source acceleration. The induced acceleration is a multiple of the gravitational potential due to the source times the acceleration of the source. It is analogous to the ##\partial A/\partial t## term in the electric field expression for electromagnetism.
At present, it is too small an effect to be confirmed experimentally, being normally swamped by the usual gravitational field, so it seems to be largely ignored. However, for a clean theoretical situation one could for example consider a test mass inside a spherical shell, where there should be no static field, and then accelerate the shell.
The induced acceleration is presumably approximately of the following form:
$$n \frac{Gm}{rc^2} \frac{dv}{dt}$$
I would like to know what ##n## is in this context. Can anyone provide a definitive reference, please? I've looked in various text books (for example MTW, Wald, Ciufolini & Wheeler "Gravitation and Inertia") and Googled without finding anything useful. I also have an old paper on frame dragging by Nordtvedt, but I don't understand it enough to extract the information I need.
If gravity was the same as electromagnetism, we would have ##n = 1##. However, the gravitational equivalent of the four-potential is a tensor quantity, so it does not transform in the same way as the electromagnetic potential. My guess is ##n = 2##, as I think the approximate equivalent of the four-potential of a moving gravitational source involves the square of the classical velocity, ##\phi(1+\tfrac{2v}{c}+\tfrac{v^2}{c^2})##, which of course does not transform as a four-vector.
At present, it is too small an effect to be confirmed experimentally, being normally swamped by the usual gravitational field, so it seems to be largely ignored. However, for a clean theoretical situation one could for example consider a test mass inside a spherical shell, where there should be no static field, and then accelerate the shell.
The induced acceleration is presumably approximately of the following form:
$$n \frac{Gm}{rc^2} \frac{dv}{dt}$$
I would like to know what ##n## is in this context. Can anyone provide a definitive reference, please? I've looked in various text books (for example MTW, Wald, Ciufolini & Wheeler "Gravitation and Inertia") and Googled without finding anything useful. I also have an old paper on frame dragging by Nordtvedt, but I don't understand it enough to extract the information I need.
If gravity was the same as electromagnetism, we would have ##n = 1##. However, the gravitational equivalent of the four-potential is a tensor quantity, so it does not transform in the same way as the electromagnetic potential. My guess is ##n = 2##, as I think the approximate equivalent of the four-potential of a moving gravitational source involves the square of the classical velocity, ##\phi(1+\tfrac{2v}{c}+\tfrac{v^2}{c^2})##, which of course does not transform as a four-vector.