Gravity Waves and Superposition?

[iramos2488]

So I heard the news today about gravity waves being confirmed. I really like learning about all the different types of waves and would like to expand my knowledge on gravitational waves. So, do gravitational waves abide by the superposition principle/property? Does anyone suggest a website or somewhere I can learn more about gravity waves.

 

[iramos2488]

Also, is a gravitational wave transverse or longitudinal?

 

[haushofer]

So, do gravitational waves abide by the superposition principle/property?

In general: No. The Einstein eqns. are highly non-linear. Only in certain cases, where you can neglect the self-interactions, does the superposition principle hold. That's why we need simulations to calculate events like colliding black holes.

 

[sanman]

In general: No. The Einstein eqns. are highly non-linear. Only in certain cases, where you can neglect the self-interactions, does the superposition principle hold. That's why we need simulations to calculate events like colliding black holes.

And yet even in spite of non-linearity, can we say that Gravitational Waves will interfere with each other, constructively and destructively?
Interference, both constructive and destructive, seems to be a feature common to all waves. Whether or not the constructive interference amounts to an exact summation, will it not still accrete?

If 2 Gravitational Wavefronts hit each other, won't it result in a somewhat larger Gravitational Wavefront?
Likewise, if 2 Gravitational Wave troughs meet each other, won't they result in a somewhat bigger trough?

(I dunno, I'm just going on intuition here, which is always a dangerous thing to do)

Could we one day have something called Gravitational Interferometry? (by this I mean interferometry done with the Gravitational Waves themselves, rather than with lightwaves)
Even if man-made Gravitational Waves would be much smaller than those generated by large Black Holes, we'd be trying to detect them at much shorter distances than those faraway Black Holes. We'd also generate them in a coherent pattern, like we do with laser interferometers.
But we'd need the equivalent of a mirror or beam-splitter to make our coherently-generated Gravitational Waves interfere with each other. How could we do that part?

 

[bcrowell]

They're transverse. They approximately obey the principle of superposition at low amplitudes -- and the amplitudes we're talking about detecting here on Earth in real experiments are extremely low.

In general: No. The Einstein eqns. are highly non-linear. Only in certain cases, where you can neglect the self-interactions, does the superposition principle hold. That's why we need simulations to calculate events like colliding black holes.

That's true for the near field, but by the time the waves get to us they are so low in amplitude that the linearized approximation is essentially perfect.

 

[haushofer]

They're transverse. They approximately obey the principle of superposition at low amplitudes -- and the amplitudes we're talking about detecting here on Earth in real experiments are extremely low.
That's true for the near field, but by the time the waves get to us they are so low in amplitude that the linearized approximation is essentially perfect.

Yes, but that's because self-interactions are then neglible, as you know. ;)

 

[pervect]

So I heard the news today about gravity waves being confirmed. I really like learning about all the different types of waves and would like to expand my knowledge on gravitational waves. So, do gravitational waves abide by the superposition principle/property? Does anyone suggest a website or somewhere I can learn more about gravity waves.

It's a tricky question - effectively, the answer at the low energy involved in the Ligo detections is yes. But at higher energies, the answer is no as several posters have mentioned. See also for instance wiki:

https://en.wikipedia.org/w/index.php?title=Pp-wave_spacetime&oldid=700066083

The fact that Einstein's field equation is nonlinear is well-known. This implies that if you have two exact solutions, there is almost never any way to linearly superimpose them.

There are books on the topic of colliding gravity waves, (most notably a specific sort of solution to Einstein's field equation, called p-p waves). See for instance the Griffiths and Bonnor references in the cited wiki article. http://homepages.lboro.ac.uk/~majbg/jbg/book/contents.pdf has the contents of Griffith's book.

To take an extreme example, singularities of various sorts are known to be able to be caused by colliding p-p waves. See for instance, Griffith's

Recent [as of the time of the writing of the book] research has clarified the singularity structure of most colliding plane wave space-times. These have been found to have a surprisingly rich variation.

I believe it would be correct to say that you could form a black hole from colliding gravity waves, for example, though I haven't found a quote that says precisely that.

 

[sanman]

They're transverse. They approximately obey the principle of superposition at low amplitudes -- and the amplitudes we're talking about detecting here on Earth in real experiments are extremely low.

Surely "low" amplitude is a relative term based on what method of measurement is used. If far more precise methods than LIGO are developed, then perhaps what is "low" today will be very much within range tomorrow. Could we one day detect Gravitational Waves from Jupiter and Saturn orbiting our Sun? If so, then perhaps we could use those wave sources to do interferometry using their Gravitational Waves. Why wouldn't that be possible?

 

[iramos2488]

In general: No. The Einstein eqns. are highly non-linear. Only in certain cases, where you can neglect the self-interactions, does the superposition principle hold. That's why we need simulations to calculate events like colliding black holes.

Einsteins eqs were well beyond the spectrum of my calc based physics courses. I remember when we learned about gravity, you know the eq something like FsubG=GMm/r^2 and was not satisfied with the explanation for gravity. (Not the equations and their effectiveness at calculating force of gravity; but just what gravity was in general. I visualize in my head and sadly after that lecture the picture in my head was pretty blank.) I theorized gravity being in the form a wave such as light and sound but now I know. I figured it would be iffy to assume G-waves acted and interacted the same as light, seeing as light and sound waves are very different. I was especially interested in superposition because there was bound to be some interference after the black holes clashed and... I guess I continue digging. Thanks so much.

 

[iramos2488]

I want to thank everybody who commented for taking time out of their day to help answer my questions. The answers to my questions have arisen new questions and I am off to dig deeper. Honestly I was just hoping my questions didnt come off as dull or limited in nature, and I was happy to see the responses. I've been amazed with einstein "the person not the brilliant mind" ever since I read "the making of a genius". It talks about how he helped a man who needed a medical procedure because he felt bad regarding his part in the a-bomb. Imagine if they put all the resources of the trinity project into gravitational research... Einstein may have lived to see his prediction hold true! THANK YOU
Cordially IramOS2488