Garth & Einstein: Examining Rotational Mass & Spacetime Distortion

[agemo]

Garth has mentioned a few times in another context that Gravity Probe B is examining whether or not a rotating mass creates a distortion in space-time in the way that Einstein's General theory of relativity predicts. (Good luck Garth for SSC… My money’s on Einstein, though…!)

I wonder if anyone has done the figures for a disk, the size of say 100 metres, so that at a given theoretical mass and rotation it creates a distortion of spacetime locally equivalent to the Earth's gravitational force?

Does anyone know any websites where this kind of thing is discussed, or have any thoughts on the subject? It seems to me that there are a few interesting things that follow.

Presumably the disk would need a few spoonfuls of rather exotic matter in order to have enough mass, even if spinning as fast as it can without breaking up.

The overall effect of the disk's rotation would make matter "fall" towards it, presumably. (Or would it be the reverse effect? A repulsive effect?)

But suppose the disk to be suspended say 10 meters above the Earth - the gravity effect of the Earth "downwards" and the disk's effect "upwards" would presumably give a resultant effect up or down to objects underneath it, depending also on how far the spacetime distortion effect of the disk reaches.

That would be worth seeing.

Presumably the disk itself would not be shielded from the Earth's gravity by its own distortion of space-time. But if this presumption is wrong, and the local disturbance caused by the disk in some way nullifies or mitigates (or even reverses) rather than amplifies the Earth's distortion of space time, the disk would expend relatively less effort escaping the Earth's gravity, (or none at all in addition to its rotation), another useful result.

In addition, what would be the effect on an object or person situated at the centre of the disk? How would the distortion of spacetime caused by the rotation of the disk operate here? For instance, would they be shielded from the disks or the Earth's gravity, or both? What would they experience if the disk accelerated, either away from the Earth or in general? Could the effects of acceleration be mitigated?

Perhaps these thoughts are all based on a simple fallacy - I'd be interested to find out. Presumably these things have been discussed somewhere. I wouldn’t know where to begin looking.

 

[pervect]

Garth has mentioned a few times in another context that Gravity Probe B is examining whether or not a rotating mass creates a distortion in space-time in the way that Einstein's General theory of relativity predicts. (Good luck Garth for SSC… My money’s on Einstein, though…!)
I wonder if anyone has done the figures for a disk, the size of say 100 metres, so that at a given theoretical mass and rotation it creates a distortion of spacetime locally equivalent to the Earth's gravitational force?

It's not clear which "distortion" you are measuring - I am guessing that you are interested in the gravitomagnetic field, the one responsible for the frame dragging effect that GP-B is measuring.

The gravitomagnetic field should be proportional to m*$\omega$, very simiar to the way that the B field of a circular current loop of radius r is proportional to I/r = qv/r = qwr/r = qw, because except for some odd factors of 2 and 4, the weak-field gravitomagnetic equations are equivalent to Maxwell's equations.

So if you were rotating 1 metric ton disk, you'd have to rotate it 6*10^21 times as fast to get the same gravitomagnetic field as the Earth. That would be 1 revolution every 1.4*10^-17 seconds. That's just not practical. A million metric ton disk would still have to rotate once every 1.4*10^-11 seconds, which is still not remotely practical.

Note that the approach I took is only approximate and won't work if the rim of the disk reaches velocites that are close to 'c'. In addition, I was calculating the B field at the center of a soleniod, gravity probe B is not located at the center of the Earth, so I ought to redo the calculation to find the magnetic field outside the current loop rather than at its center. Being lazy, and because we are so many orders of magnitude away , I'm not going to bother with this calculation.

Basically, the Earth will provide a much bigger gravitomagnetic field than anything we can set up in a laboratory.

I'm afraid I don't quite follow the rest of your questions, hopefully this will give you some insight into the matter.

 

[agemo]

thanks

Thanks,
that's exactly what I was looking for. I thought it would be harder to calculate. So only if you took a lot of pretty exotic matter and got a mass of 10^12 or so tonnes would you be likely to produce the effect.

I was wondering how such a thing would effect objects around it.

Cheers

agemo