Question about gravity, frame dragging, and the dynamo effect.

[DandelionTheory]

I'm not sure this is in the right spot, but here it goes.

2 massive objects in space, object A has an angular momentum of X, while object B has an angular momentum of 0 in relation to the stars.

the question is when does object A induce object B to have an angular momentum or greater than 0 in relation to the stars? When or does the dynamo effect apply?

I attempted to find my answer within the explanations of frame dragging and I got as far as "list".

thank you in advance.

[Markus Hanke]

5 hours ago, DandelionTheory said:

the question is when does object A induce object B to have an angular momentum or greater than 0 in relation to the stars?

The rotating object would “drag along” object B in its direction of rotation (frame dragging), so that object would gain orbital angular momentum as seen by a far-away observer. Whether it would itself start to rotate around its own axis is a question that is not so easy to answer, since the two-body problem in Kerr spacetime is a notoriously difficult problem. 

I don’t know what you mean by “dynamo effect” though, as that usually refers to how magnetic fields are generated.

[DandelionTheory]

Thank you.

Another question: say object B starts with an angular momentum on it's axis, would the frame dragging effect from A to B "stack" with the frame dragging effect generated by object B?

[DandelionTheory]

I'm replying again to address the rest of your question. I was referring to the assumed hypothetical that the dynamo effect could apply somewhere in the answer, but in order for that to apply both objects would need a magnetic field for a torque to be induced. I'm assuming.

 

[Markus Hanke]

10 hours ago, DandelionTheory said:

Thank you.

Another question: say object B starts with an angular momentum on it's axis, would the frame dragging effect from A to B "stack" with the frame dragging effect generated by object B?

When you have two rotating objects orbiting one another, then each of them will have an influence on the geometry of spacetime. But this combination will be a highly non-linear and complex affair, so it’s not possible for me to tell exactly how this would look like.

5 hours ago, DandelionTheory said:

I'm replying again to address the rest of your question. I was referring to the assumed hypothetical that the dynamo effect could apply somewhere in the answer,

The dynamo effect is a mechanism by which magnetic fields are generated in the interior of rotating bodies, such as planets. I do not see the connection to frame dragging.

[Strange]

2 hours ago, Markus Hanke said:

The dynamo effect is a mechanism by which magnetic fields are generated in the interior of rotating bodies, such as planets. I do not see the connection to frame dragging.

That raises a question: would frame dragging affect the magnetic field of a charged rotating black hole? And, more generally, do we know how to apply Maxwells equations in curved space time?

[Markus Hanke]

21 hours ago, Strange said:

That raises a question: would frame dragging affect the magnetic field of a charged rotating black hole? And, more generally, do we know how to apply Maxwells equations in curved space time?

The answer is yes to both. Maxwell’s equations can very easily be generalised to curved spacetimes; in fact all you need to do here is write them in terms of the differential forms formalism, which is fully covariant. Likewise, EM fields function as sources of gravity - all you need to do here is insert the stress-energy tensor for the electromagnetic field into the Einstein equations.

Ideally one of these (either a metric, or an EM field) will be given, and you can then calculate the other. If you know only a distribution of sources, but neither metric nor EM field, then you will need to solve a system of equations that comprises both the Maxwell and the Einstein equations. This is potentially very challenging, mathematically speaking.

But yes, EM fields influence the geometry of spacetime, and the geometry of spacetime influences EM fields. It’s a pretty complex and non-linear “feedback system”. 

[DandelionTheory]

On 8/13/2018 at 10:49 PM, Markus Hanke said:

When you have two rotating objects orbiting one another, then each of them will have an influence on the geometry of spacetime. But this combination will be a highly non-linear and complex affair, so it’s not possible for me to tell exactly how this would look like.

Hrm, I should add more parameters to the example. 

Given: 4 massive objects in space, A, B, C, D, positioned in a 2x2 pattern with center point Q; A and B, C and D. L distance from one another. Each with rotation about there respective central axis, and each axis of rotation is parallel to each other. 

Lets talk about the concept of "rolling over" frames. If each objects angular momentum drags on the space around it, there is only the factor of effective range we have to worry about. If objects A-D rotated the same direction there would be little change to any space around. If, on the other hand, objects A-D orbit point Q with no rotation about there respective axis, there would be a larger average effective range after a certain angular momentum is reached. Now lets do something weird, lets fluctuate the objects angular momentum in tandem (Ex: from a momentum of 4 to 7 to 4 back to 7 and so on), essentially attempting to drag space from one side of the system to another. I personally would do this by pulsing gravity like an electromagnet. To myself this example resembles an AC motor, but here the "excited poles" would be the objects relative change in mass to an outside observer and the magnetic field would be the frame dragging effect induced on the space directly outside the circumference of rotating masses.

Question: after recovering from the shear awe caused by that thought experiment, I thought this would be interesting to use like wire in a coil. But I need to know if frame dragging "stacks" or "rolls over" so the next object's frame drag blurs into the other. sort of like how multiple turns of wire shapes the magnetic field into a larger one when current is applied. So, does frame dragging "roll over"?

After thought, purely speculative: I would suspect the higher the total number of objects used in the example, the lower the angular momentum of the system needs to be in order to achieve the roll over effect.

On 8/13/2018 at 10:49 PM, Markus Hanke said:

The dynamo effect is a mechanism by which magnetic fields are generated in the interior of rotating bodies, such as planets. I do not see the connection to frame dragging.

My logic comes from rotating bodies being the source of frame dragging, and magnetic fields have this weird property on charged masses. They rotate.

Edited August 15, 2018 by DandelionTheory

[beecee]

20 hours ago, Markus Hanke said:

On 8/14/2018 at 6:18 PM, Strange said:

That raises a question: would frame dragging affect the magnetic field of a charged rotating black hole? And, more generally, do we know how to apply Maxwells equations in curved space time?

The answer is yes to both. Maxwell’s equations can very easily be generalised to curved spacetimes; in fact all you need to do here is write them in terms of the differential forms formalism, which is fully covariant. Likewise, EM fields function as sources of gravity - all you need to do here is insert the stress-energy tensor for the electromagnetic field into the Einstein equations.

Ideally one of these (either a metric, or an EM field) will be given, and you can then calculate the other. If you know only a distribution of sources, but neither metric nor EM field, then you will need to solve a system of equations that comprises both the Maxwell and the Einstein equations. This is potentially very challenging, mathematically speaking.

But yes, EM fields influence the geometry of spacetime, and the geometry of spacetime influences EM fields. It’s a pretty complex and non-linear “feedback system”. 

While I understand that charge, mass and angular momentum are the only three properties a BH can have, charge would be quickly negated, would it not? and over far longer periods of time, so to would angular momentum. In other words the Schwarzchild metric while obviously being the simplest, is also the end state of all BH's.

[Markus Hanke]

8 hours ago, DandelionTheory said:

But I need to know if frame dragging "stacks" or "rolls over" so the next object's frame drag blurs into the other.

I think what you are asking is whether solutions to the gravitational field equations linearly superimpose (like EM waves do). The answer is no, unfortunately. Unlike electromagnetism, gravity is a non-linear affair - this means that the effects of the rotating bodies will combine in some way to yield an overall metric of spacetime, but this combination is not a linear superposition, but something much more complicated. Having four charged, rotating bodies in General Relativity is a scenario so complex that it could only be solved numerically (and would require substantial computing power to do so).

3 hours ago, beecee said:

charge would be quickly negated, would it not?

Yes, it generally would.

3 hours ago, beecee said:

and over far longer periods of time, so to would angular momentum.

I’m not so sure about this one. But what mechanism would it get neutralised? In either case, this does not appear to be what we observe around us.

3 hours ago, beecee said:

In other words the Schwarzchild metric while obviously being the simplest, is also the end state of all BH's.

The Schwarzschild solution requires spacetime to be everywhere empty and asymptotically flat. This is not a situation that we will ever find in the real world, except as an approximation. No black hole can ever be perfectly Schwarzschild.

[beecee]

24 minutes ago, Markus Hanke said:

I’m not so sure about this one. But what mechanism would it get neutralised? In either case, this does not appear to be what we observe around us.

I was thinking along the lines of matter falling in, and accretion disk interactions...I would hazard a guess and say depending on trajectory etc, that this could also spped up angular momentum.

Quote

 The Schwarzschild solution requires spacetime to be everywhere empty and asymptotically flat. This is not a situation that we will ever find in the real world, except as an approximation. No black hole can ever be perfectly Schwarzschild.

Hmmm, can you elaborate on that answer a bit? Again, my thoughts are that it would be the natural end state, well into the future [hundreds of billions of years] and prior to BH evaporation via Hawking Radiation process.

[Markus Hanke]

22 hours ago, beecee said:

I was thinking along the lines of matter falling in, and accretion disk interactions...I would hazard a guess and say depending on trajectory etc, that this could also spped up angular momentum.

I wouldn’t think so, since all objects we observe around us carry some form of angular momentum. It doesn’t seem as if such a cancelling out is happening.

23 hours ago, beecee said:

Hmmm, can you elaborate on that answer a bit? Again, my thoughts are that it would be the natural end state, well into the future [hundreds of billions of years] and prior to BH evaporation via Hawking Radiation process.

The thing is that the Schwarzschild solution requires spacetime to be empty and asymptotically flat, neither of which is a situation we actually find in the real world (except as an approximation). It is also stationary, which excludes any evaporation processes, or any changes at all to the black hole over time.

I think in terms of real-world finding, a Vaidya-type spacetime is far more realistic - specifically, the Vaidya-Bonnor-Kerr metric could be a good model of the natural end state of a black hole.

[beecee]

53 minutes ago, Markus Hanke said:

I wouldn’t think so, since all objects we observe around us carry some form of angular momentum. It doesn’t seem as if such a cancelling out is happening.

So the  Reisner-Norstrom BH is just a theoretical  idealised solution, not evidenced?

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The thing is that the Schwarzschild solution requires spacetime to be empty and asymptotically flat, neither of which is a situation we actually find in the real world (except as an approximation). It is also stationary, which excludes any evaporation processes, or any changes at all to the black hole over time.

OK this confuses me....I would have thought any BH is defined by some mass, which critically curves the spacetime it is embedded in. I understand that it is a solution to Einstein's field equations with the simplest outcome for convenience.     https://en.wikipedia.org/wiki/Schwarzschild_metric

Please alleviate my confusion!! Remember as a lay person I need to be treated gently...like a virgin if you will. 

 

Quote

I think in terms of real-world finding, a Vaidya-type spacetime is far more realistic - specifically, the Vaidya-Bonnor-Kerr metric could be a good model of the natural end state of a black hole.

Ahaa! something I have learnt today!! I have not previously been aware of the  " Vaidya" or Vaidya-Bonnor metric.....Thanks.

I must say at this stage most of what I do know about BH's was gained a decade or more ago, and I certainly have not done to much brushing up with reputable reading to add to that past knowledge.

Edited August 17, 2018 by beecee

[Markus Hanke]

1 hour ago, beecee said:

So the  Reisner-Norstrom BH is just a theoretical  idealised solution, not evidenced?

I may be wrong on this (someone correct me, if so), but I think there has not actually been any observations of electrically charged black holes (or any other body with substantial net charge, for that matter). It may still be possible for this to happen during short periods of time, but I think such net charge would be neutralised fairly quickly.

1 hour ago, beecee said:

I would have thought any BH is defined by some mass, which critically curves the spacetime it is embedded in. I understand that it is a solution to Einstein's field equations with the simplest outcome for convenience.

Actually, the Schwarzschild solution is just a 1-parameter family of metrics that arises from the field equations for a certain set of boundary conditions - one amongst which is asymptotical flatness. It is also a vacuum solution, so the energy-momentum tensor vanishes everywhere in this spacetime. We identify the one free parameter that appears as “mass”, but that is not a source that is part of the manifold, and that identification with mass arises from boundary conditions (specifically, from the demand that Newtonian gravity is reproduced at infinity). As such, the mass is actually a global property of the entire spacetime, not of any body within it.

[beecee]

11 hours ago, Markus Hanke said:

I may be wrong on this (someone correct me, if so), but I think there has not actually been any observations of electrically charged black holes (or any other body with substantial net charge, for that matter). It may still be possible for this to happen during short periods of time, but I think such net charge would be neutralised fairly quickly.

I would 100% agree with charge being neutralised pretty quickly,  it was the static solution [zero angular momentum] that had me somewhat disturbed. But as you say, probably never been observed.

Quote

Actually, the Schwarzschild solution is just a 1-parameter family of metrics that arises from the field equations for a certain set of boundary conditions - one amongst which is asymptotical flatness. It is also a vacuum solution, so the energy-momentum tensor vanishes everywhere in this spacetime. We identify the one free parameter that appears as “mass”, but that is not a source that is part of the manifold, and that identification with mass arises from boundary conditions (specifically, from the demand that Newtonian gravity is reproduced at infinity). As such, the mass is actually a global property of the entire spacetime, not of any body within it.

OK, I believe I can live with that...thanks for the answers and clearing up a couple of misconceptions.

[Markus Hanke]

15 hours ago, beecee said:

OK, I believe I can live with that...thanks for the answers and clearing up a couple of misconceptions.

When I first learned about GR, the notion of some free parameter in the metric (such as mass, charge, angular momentum) being a property of spacetime itself rather than any material body in it, took me quite some time to get my head around. But it is what it is.