What Does the Gravitomagnetic B-Field Describe and What Are Its Units?

[stubbypeeps33]

Does the gravitomagnetic B-field (from the GEM equations) have units of frequency (1/s)? And if so, what exactly does the B field describe?

I guess what I'm really trying to find out is whether the B field around say a rotating spherical object describes the rate of frame dragging, or does it describe how a particle near it will spin around its own axis, or something entirely different?

And also why is it that because gravity is a spin-2 field, the gravitomagnetic charge is twice that of the gravitoelectric charge?

Thanks,

stubby

 

[Mentz114]

Hi stubby,

can you give a reference to put this in context ? I don't know about GEM but in GR the field around a rotating body will induce rotation in test bodies. See Hamilton and Lyle arXiv:gr-qc/0411060v2.

M

 

[Jonathan Scott]

Does the gravitomagnetic B-field (from the GEM equations) have units of frequency (1/s)? And if so, what exactly does the B field describe?

I guess what I'm really trying to find out is whether the B field around say a rotating spherical object describes the rate of frame dragging, or does it describe how a particle near it will spin around its own axis, or something entirely different?

And also why is it that because gravity is a spin-2 field, the gravitomagnetic charge is twice that of the gravitoelectric charge?

Thanks,

stubby

There are various different conventions for the gravitomagnetic B-field, differing by factors of 2. However, they all effectively represent an angular velocity. Basically, if you are in such a field, you feel as if you are rotating, in the same way as if you're in the E-field component, you feel as if you are accelerating. The rotation can be detected for example by rotational frame-dragging of a gyroscope.

The gravitomagnetic equations can't be matched up exactly with the electromagnetic equations; one way or another there's always a factor of 2 needed somewhere, and different sources use different conventions. (Last time I looked, the Wikipedia entry on the subject was not even self-consistent). This does seem to relate to the need to use a tensor rather than a vector as part of the description of the force between relatively moving objects. However, I don't personally know how this relates to "spin 2".

For more details on GEM, I suggest you Google "gravitomagnetism" and have a look at the 2000 review paper by Mashhoon. There seems to be a more recent paper too, but I haven't looked at that.