# Gravitational waves and refraction patterns...

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## Main Question or Discussion Point

I was doing a thought experiment last night. Gravitational waves, being like any other type of wave would cancel each other out and create a refraction pattern of strength.
While we do not have definitive proof there is a black hole at the center of every Galaxy, we do know, through observations, that there are many stars, tightly compacted as compared to the edges. Could the gravity from this cluster of stars be creating gravitational waves that spread out and cancel each other out causing gravity in a Galaxy to be spread evenly? Could this explain why stars at the edge of Galaxies move at the same speed around the galaxy as the stars that are closer?
Thanks,
Ben

Khashishi
No. You can think of the gravitational field as somewhat analogous (at low field strength) to the electromagnetic field. The field can be separated into a near field and radiation. The near field part is responsible for all the orbital mechanics you see in the galaxy. This is a static attractive field. This part doesn't propagate as a wave. Since it's all attractive, there isn't any cancellation.

Only the radiation propagates as a wave, and it is very weak. The radiation is too weak to have any effect on the galactic orbits.

Thanks, that makes sense.

I also am curious about the behaviour of GW's. It now seems accepted that they move at velocity of light and convey energy /momentum as do EM waves. How far can parallels be drawn on GW behavior with EM waves. For example would they be refracted, slowed, etc in an appropriate medium. If so what would an appropriate medium consist of, my guess would be a field of mass (particles).

PeterDonis
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It now seems accepted that they move at velocity of light and convey energy /momentum as do EM waves.
Yes, although the analogy is not exact, since EM waves have nonzero stress-energy but GWs have zero stress-energy; they are "made of" spacetime curvature and nothing else.

How far can parallels be drawn on GW behavior with EM waves. For example would they be refracted, slowed, etc in an appropriate medium. If so what would an appropriate medium consist of
If you think of spacetime geometry as the "medium", many parallels work pretty well, at least at the heuristic level. So, for example, a region with stronger spacetime curvature (such as near the horizon of a stellar mass black hole) would be expected to refract GWs passing through it.

The caveat with this kind of viewpoint is that since, as above, GWs themselves are made of spacetime curvature, there is no way to fully separate a complete spacetime geometry into the part that is "gravitational waves" and the part that is "the medium in which the gravitational waves propagate" (the latter is often called the "background spacetime"). There are cases of interest (such as analyzing binary pulsars) in which you can make a very good approximate split, but there is always some residual ambiguity about exactly what spacetime curvature is "GWs" vs. "medium". This is different from the case of EM waves, where the "medium" is again spacetime, but the "waves" themselves are made of stress-energy (electromagnetic fields), so the separation between the two is exact and there is no possibility of mixing them up.

First thank you very much for your response - and apologies for my delay in getting back -thinking about new things takes time in my case.

So a GW has no stress/ energy but does have energy 'represented' by its curvature.

I have understood what you have said as - GW's will be influenced by the curvatures in spacetime and they will influence whatever curvatures they 'flow through'. So in the case you mention of GW interacting with a spacetime near a black hole the curvatures of both will determine the outcome. If the GW has weak curvature the GW near the BH will tend to move along null geodisics but at large distances from the BH where its curvature is very low the situation may be completely different.

On the above basis I think I follow what you are saying about a spacetime medium, the concept only makes sense if the object you are discussing has low curvature compared to the background at the point you are interested in. If the curvatures of the 'interacting' parts are similar, a picture using a medium would be useless. But you do mention the binary pulsars where a good approximate split is possible which does contradict what I have just said - I will follow this up when I have a better understanding of the basics in GW's. On the difference between EMwaves/stress energy and GW/curvature I can see that the sources are different even though both result from accellerating mass (EM requiring the added ingredient of charge). The common feature of accellerating mass does suggests to me that a (very feeble) GW must always be created with an EM wave.

I should perhaps mention my motivation for asking the question. I have only a basic understanding of GW but was interested in their properties in respect of their affect on collapse of gas clouds. Some preliminary thoughts suggested that the transverse components of GW should make no difference to a clouds rate of collapse but some cloudy thinking on my part suggested that the transverse components and absense of a londitudinal component in a GW would make a difference. The question was an attempt to look at the problem in a different way. Einstines original longditudinal/transverse GW's would probably be better suited to creating what I had in mind but I suspect nobody is considering putting those back on the shelf.

Once again thanks for your help and I would be very grateful for your comments on where I have missed on points you were making - thinking about clouds is OK but cloudy thinking is best corrected!

PeterDonis
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apologies for my delay in getting back
No apology is needed. We don't have any fixed time schedules here. It's always understood that you can take as long as you need to to think through something before you respond. In fact, we much prefer that you think it through before you respond, since that is likely to make your response much more productive.

PeterDonis
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2019 Award
If the GW has weak curvature the GW near the BH will tend to move along null geodisics but at large distances from the BH where its curvature is very low the situation may be completely different.
This is not quite correct. The standard theory of GWs (i.e., the one we know how to solve with actual equations instead of having to just have supercomputers crunch approximate numbers ) assumes that the GW is weak in the sense that its corrections to the background metric are much smaller than the background metric itself. This is not the same as saying that the curvature of the GW is much smaller than the curvature of the background metric; for example, in the most common case, the background metric is Minkowski spacetime, which is flat (zero curvature), so any curvature at all due to the GW will be larger. But the Minkowski metric itself has a value of $\pm 1$ on the diagonals, and a weak GW in Minkowski spacetime will have corrections to the metric that are much smaller than $1$. (The technical term for this theoretical approach is "linearized gravity".)

you do mention the binary pulsars where a good approximate split is possible which does contradict what I have just said
Not with the correction above. In the binary pulsar case, the background metric is not constant; it changes with time, and the changes are related to the energy being carried away by gravitational waves. But what I said above is still true for this case: the corrections to the background metric due to the GWs are much smaller than the background metric itself.

If it helps, you might consider a simpler case such as a spherical planet about the size of the Earth with ocean everywhere on its surface, and waves on the ocean. The average spherical geometry of the ocean's surface is like the background spacetime, and the waves on the ocean are like the gravitational waves. Their size will be much smaller than the size of the planet, which corresponds to the GWs being weak. (This analogy is limited because it leaves out time, but it might help to visualize what is meant by a "weak" GW.)

The common feature of accellerating mass
It's not quite a common feature, because "accelerating mass/charge" is not precisely the right term for the source in either case, and the correct sources are different in the two cases.

In the EM case, it turns out to be the third time derivative of the position of the charge (more precisely, of the charge dipole moment--see below) that produces EM waves. This is obscured in the most common case, charges in circular motion (such as electrons moving in a magnetic field), because it turns out that in that particular case, the third time derivative and the second time derivative have a fixed relationship, so you can substitute one for the other in the equation and make it look like it is just the acceleration driving the waves. But when you look at other cases, this breaks down and you have to go back to the more basic equation that has the third time derivative.

In the GW case, the source is still the third time derivative, but now it's the third time derivative of the mass quadrupole moment (as opposed to the charge dipole moment for the EM case). This means that some cases even of circular motion of mass will not generate GWs, where the equivalent circular motions of charge would generate EM waves.

For both GW and EM, constant linear acceleration produces zero waves; this is another illustration of the fact that it's the third time derivative, not the second, that matters.

I have only a basic understanding of GW but was interested in their properties in respect of their affect on collapse of gas clouds.
In practical terms, this is negligible; GW emissions in such cases can occur in principle, but they will be so many orders of magnitude smaller than other emissions (EM waves and even direct ejections of mass from the cloud) that they will have no appreciable effect on the overall process.

PeterDonis
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2019 Award
Einstines original longditudinal/transverse GW's
Those were an artifact of an earlier attempt at a relativistic theory of gravity, one which Einstein had to abandon.

I suspect nobody is considering putting those back on the shelf.
That would be correct, since they are not part of GR, they are part of an earlier failed attempt at a relativistic theory of gravity (see above).

Thanks for the responces these will take me a while to work through.

On the question of EM wave generation you definitely gave me a bit of a jolt pointing out that EM radiation is not generally the result of accellerations but I suspect it was Proff Feynman who gave everyone the initial jolt when he pointed to the second term in his radiation reaction formulae. Point taken EM radiation is not attributable to accellerating charges

Peter, I finished writing the stuff bellow on saturday night, circuits cooking but sadly none burnt out. It is based on the seed that arrived with your response. Regardless of the size of the possible effect ( GW's created at particle pair creation must have micoscopic curvature/energy and cosmic scale wavelength(/curvature?)) I am always compelled to follow it through. I normally bin the ideas (in private) when they get to this stage, but this came with a possible (??) experiment which is not always the case and I would have had to write something else that would have been bland as well as being drivel.
Oh, and apologies for the excursions.
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On EM radiation emmission I looked at
http://www.mathpages.com/home/kmath528/kmath528.htm
which seemed a good starter. But this gives me the impression that many think the matter is not settled. I realised I had been here before many years ago when I had Griffiths - EM, Excellent texbook (no longer have it or any textbook sadly), I also have a memory of seeing some reference to papers he had written on this subject (I have never looked at them- oh - apologies to the above if I have this wrong)

Radiations from moving particles include Cyclotron, synchrotron, Cherenkov, with reverse Cherenkov and Askaryan. I had never heard of the last 2 before looking them up in Wikipedia (its good for a quick reference). Looking at the equations it is instantly obvious that they do not included all the accellerations! For example one constant - earth's gravity is ignored. Whilst this may be considered a slight perturbation in comparison with the large background created by the machine, it is always nice to see all effects accounted for before dismissing them (ha).

I have decided to stop looking up papers on this subject for the time being as this topic is getting far too interesting and I am in danger of moving onto a tangent plane and getting wrapped up in the tightly curved spaces others have left there. There is a lot to be said for the old days when there were just text book and papers not a plethera of money spinning "science for the masses" books that tell you very little. The WWW is also probably a total distraction unless used well ( a difficult thing to do) then it is absolutely wonderful and you wonder how people could ever have know anything much before its invention.

Sorry one last thought (yes I have fallen onto the tangent plane). At particle creation there will be a jolt possibly of the third degree or more. The jolt will presumably induce a GW (or maybe 2 GW's). The GW should propagate at a greater velocity than the particle. If an observer tests the particles' properties one would imagine that the GW would be long gone. But whilst GW's do not observably effect matter much (solved my other problem- maybe), it is probable that they do interfere with each other and themselves (I have only read some bits on this). Such interference could have effects on group velocity. However if the group velocity were the same as the particle velocity this would be interesting for the observer of a particle and could even induce a bit of wobbling of the particle as it moves. If there was another observer of the other particle a comparison of properties would also be interesting if there was a way to affect a GW.

On hearing the words linearized gravity comprehension has returned. Most of what you have said is now fairly clear to me. Your analogy with an ocean on a planet is attractive as I have spent considerable time on the oceans. I was once in a 10+ m sea with 45Kn winds and whilst we experianced rough motion we remained very upright. On another occassion in a flat calm sea a small ferry turned as he approached us generating a short unusual looking wavetrain less than 1m high. On contact with the wave our boat turned onto its beam with the top of the mast nearly touching the water. So it would seem to me that even a small but varying metric may have significant effects if resonance comes into play.

So GW's depend upon the third derivative of the quadrupole of mass charges. I had never really thought much about quadrupoles before so I looked at
http://astrowww.phys.uvic.ca/~tatum/elmag/em03.pdf
Thinking I knew enough about dipoles I went straight to the quadrupole section. They had put in some nice diagrams which are always a good start. The first diagram had a line with 3 blobs on it. At each end of the line was a charge of -Q and in the middle was a charge of +2Q. My instant thought was that they had misplaced the diagram from the tripole section (ha!). Fortunately some understanding dawned and I will probably have to re-read the basics of CMB.

There is one thing about GW's that I can predict with almost total certainty , that is the maths will be very hard. I have resisted delving into them at this stage. Its not that I dislike the maths - I enjoy(ed) it immensly, but my maths processor has seized from many decades of non-use. Many of the papers I have attempted to read are also so poorly written with undefined element and statements like "it is clear ..." as though they are having a chat with the people in the next room who know everything about it. These days I read the abstract and if that looks sufficiently intersting I read a para or 2, if they are unable to properly set out their thoughts I stop and find someone who can. (Oops - tut tut)

On the longditudinal/transverse GW model that died, I had no great interest in resurrecting it but I was curious as to its cause of death. As part of the hunt for the quadrupole I had attempted to construct a GW simulator. I thought rather than rattling the charge (in a third derivative way) I might rattle the coil - well this sort of thing had seemed to produce interesting results on a few occasions. I came up with two models neither of which produced the exact effects. One required rotation and produced a rotating GW and both have a longditudinal additive. The fun version requires one imaginary box (not rotating- just wobbling -in a relative way) and a sequence of masses. The box moves on a sequence of hyperbolic orbits passed the masses. Well at that point I could not get rid of the longiditudinal component (infinite planes are difficult to join together - and square GW's!) - hence the question.

The latest version looks better (joining infinite planes is easy). Take one very long massless tube and wrap a very long massive rod around it. Make one small cylindrical box of diameter smaller than the tube (it tends to wobble around- different wobble this time- no similar to above) and propel it through the tube. Before conducting experiments in the box I was hoping for an opinion on whether the metric in the box conforms to a rotating GW. If so the arrangement may also function as a GW modifier which could be useful.

Oops sorry Peter I seem to be lost again - do you know where the exit tensor is up here?
__________

PeterDonis
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2019 Award
On the longditudinal/transverse GW model that died, I had no great interest in resurrecting it but I was curious as to its cause of death.
The earlier relativistic theory of gravity on which it was based made other obviously wrong predictions (IIRC one was that it did not correctly predict the additional precession of Mercury's perihelion), so Einstein dropped it and tried another. There was nothing in particular about the GW part of that earlier theory that caused problems, since nobody at that time had ever observed anything even remotely attributable to GWs and they were not a theoretical prediction of Newtonian gravity so nobody had really thought about them.

Thanks very much for the information- I think I may have confused it with his later retraction of GW and subsequent reinstatement.

I am also back on the trail so hopefully you will find a bullet for the GW modifier (my shotgun is empty) and save my circuits from re-heating.

The implications of GW emission from actions on matter and possible absorbtion by matter seem very far reaching. It is difficult to identify parts of fundemental physics they would not effect. My list of areas of interest starts with inertia and covers much of the rest.