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View Full Version : Dark matter vs frame dragging, has anyone done the math?



wiggy
2012-Sep-10, 08:43 AM
I heard Fraser say that the accretion disc of a black hole has a surface speed approaching the speed of light.

If we can measure frame dragging around the earth with such a small mass and a low surface speed, how large is the affect of frame dragging around a super massive black hole with a surface speed of 0.999999999C?

Could this frame dragging be enough to give the illusion of a galaxy spinning too fast for its mass?

I've never hear of this particular factor being discussed when discussing the hypothesis behind dark matter.

If we're looking down on a galaxy and its time space has been twirled up like spaghetti on a fork, would that explain what where seeing?

Just asking, I have no idea of the strength of frame dragging, like how far out the influence of it is.

Jeff Root
2012-Sep-10, 09:03 AM
A very simple, but, I think, completely adequate answer:
Frame dragging has no effect at all far from the black hole.
At the event horizon the frame dragging is total, a few
radii away it is zero.

-- Jeff, in Minneapolis

wiggy
2012-Sep-11, 09:01 PM
thanks jeff,
I had no model in my head of how far its influence spread. I would love to see an animation one day of how the background would distort as you approach something like that.

caveman1917
2012-Sep-11, 09:53 PM
It would also give the wrong dynamics, since the frame dragging effects also drop off with distance, it would make the innermost stars orbit "too fast" while the dark matter problem is that the outermost stars are orbiting "too fast".

utesfan100
2012-Sep-11, 10:11 PM
It would also give the wrong dynamics, since the frame dragging effects also drop off with distance, it would make the innermost stars orbit "too fast" while the dark matter problem is that the outermost stars are orbiting "too fast".
Would I be wrong to think that frame dragging dies off like magnetism, at 1/r^3, faster than the Newtonian 1/r^2?

I know that rotation curves need a force that dies off at 1/r.

antoniseb
2012-Sep-11, 11:25 PM
Would I be wrong to think that frame dragging dies off like magnetism, at 1/r^3, faster than the Newtonian 1/r^2?


It goes as 1/r^3 in a weak field, such as far removed from the dense object, but in a relativistically strong field it is still about 1/r^3 but the formula is more complicated. Your assessment of its value replacing dark matter is accurate... it is very much the wrong formula.

Cougar
2012-Sep-12, 12:44 AM
Your assessment of its value replacing dark matter is accurate... it is very much the wrong formula.

Both very astute assessments! Going only slightly off-OP, what about frame-dragging's 'cousin', gravitational waves? Ripples in spacetime apparently carry some ability to do work. This would seem to imply a modicum of energy....

wiggy
2012-Sep-12, 08:15 AM
It would also give the wrong dynamics, since the frame dragging effects also drop off with distance, it would make the innermost stars orbit "too fast" while the dark matter problem is that the outermost stars are orbiting "too fast".

D'OH of course. :) excuse me, I'm just going out the back to slap myself.

caveman1917
2012-Sep-12, 10:19 PM
Both very astute assessments! Going only slightly off-OP, what about frame-dragging's 'cousin', gravitational waves? Ripples in spacetime apparently carry some ability to do work. This would seem to imply a modicum of energy....

Whilst it is true that the power lost to gravitational waves is larger for the innermost stars (the power goes like 1/r^5) this effect is so tiny that it is completely lost in the background noise. Also gravitational waves only come up in GR, not in Newtonian gravity, and the dark matter problem appears in a purely newtonian treatment (a GR treatment of a galaxy would be intractable).

Last but not least the effect of the power lost to gravitational waves is in decreasing the radius of the orbit, which in turn increases the orbital speed, it does not slow down the orbital speed. If this effect were significant we'd expect to see the density profile more sharply increasing towards the center of galaxy but no effects looking like there is something wrong with the gravitational force itself.