- #1
Sonderval
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I have the following question considering frame dragging:
A test mass starting at rest near a rotating mass or with an initial velocity pointing towards the center of the rotating mass will be deflected in such a way that it begins to move around the mass in the rotational direction. This is normal frame dragging.
Now consider the opposite situation: A test mass starts near the rotating mass but is moving outwards with a velocity in radial direction. In which direction would this mass be deflected?
According to standard formulations of gravitoelectromagnetism like here
http://www.arxiv.org/abs/gr-qc/0311030
the acceleration is proportional to v×B (with B being the analogue of the magnetic field); so if I reverse the velocity, the acceleration should be reversed as well, i.e., if a moving mass is deflected to the right relative to its velocity on falling in, a mass moving out should also be deflected to the right relative to its velocity.
But when I try to see this effect (for example using the program GRorbits
http://stuleja.org/grorbits/), the outwards moving mass is deflected in the co-rotating direction.
So I'm confused which answer is correct and where the mistake in my argument concerning the cross-product lies, if there is one.
I suspect that part of the problem may be that the "outward radial direction" depends on whether I look at the situation from the point of view of a distant Schwarzschild observer or a local frame, but I am not exactly sure how to see this more clearly or make this idea exact.
A test mass starting at rest near a rotating mass or with an initial velocity pointing towards the center of the rotating mass will be deflected in such a way that it begins to move around the mass in the rotational direction. This is normal frame dragging.
Now consider the opposite situation: A test mass starts near the rotating mass but is moving outwards with a velocity in radial direction. In which direction would this mass be deflected?
According to standard formulations of gravitoelectromagnetism like here
http://www.arxiv.org/abs/gr-qc/0311030
the acceleration is proportional to v×B (with B being the analogue of the magnetic field); so if I reverse the velocity, the acceleration should be reversed as well, i.e., if a moving mass is deflected to the right relative to its velocity on falling in, a mass moving out should also be deflected to the right relative to its velocity.
But when I try to see this effect (for example using the program GRorbits
http://stuleja.org/grorbits/), the outwards moving mass is deflected in the co-rotating direction.
So I'm confused which answer is correct and where the mistake in my argument concerning the cross-product lies, if there is one.
I suspect that part of the problem may be that the "outward radial direction" depends on whether I look at the situation from the point of view of a distant Schwarzschild observer or a local frame, but I am not exactly sure how to see this more clearly or make this idea exact.