Gravity Waves vs Elastic Sheet: Is the Analogy Productive?

[pervect]

The basic question was inspired by some other recent threads on the "fabric of space". If we imagine a 2-d spatial rubber sheet, how closely can we make its vibrational modes compare to gravity waves (in the limit of non-relativistic velocities).

It's well known that gravity waves locally stretch in one direction and compress in the other, I would assume this would place some constraints on Poisson's ratio of our hypothetical material.

Is this even possible at all, or is the analogy unproductive if we try to take it too seriously? As I recall, there are no spherically symmetric gravity waves, but if we drop a pebble on a sheet, we expect as a primary mode spherically symmetric ripples.

 

[Vanadium 50]

I don't think this will work. The rubber waves are fundamentally dipole in nature and gravitational waves are fundamentally quadrupole.

 

[Ich]

I think you need at least a 3D-body with Poisson's ratio 0.5 to conserve the volume. It wouldn't work, though. Imagine a plane wave: You have deflections proportional to transverse distance, that means arbitrarily large. If you want to simulate this with real, proper acceleration, you have to reduce the frequency accordingly to zero.
I could imagine a quadrupole deformation propagating along a tube, but I'm not sure about this.

 

[m4r35n357]

The basic question was inspired by some other recent threads on the "fabric of space". If we imagine a 2-d spatial rubber sheet, how closely can we make its vibrational modes compare to gravity waves (in the limit of non-relativistic velocities).

It's well known that gravity waves locally stretch in one direction and compress in the other, I would assume this would place some constraints on Poisson's ratio of our hypothetical material.

Is this even possible at all, or is the analogy unproductive if we try to take it too seriously? As I recall, there are no spherically symmetric gravity waves, but if we drop a pebble on a sheet, we expect as a primary mode spherically symmetric ripples.

http://en.wikipedia.org/wiki/Gravity_wave

Sorry, couldn't resist ;)

 

[haael]

If we imagine a 2-d spatial rubber sheet, how closely can we make its vibrational modes compare to gravity waves

Rubber sheet gets deformed in the dimension perpendicular to the sheet and is a good model of a scalar field.

Sound waves are displacements in the dimension(s) parallel to the sheet, so they are a good model of a vector field.

Gravitational waves are a spin-2 tensor field. The best analogy I saw looks like the metal net used for fences:

Its modes of vibration look a bit like that:

This is the closest analogy of a spin-2 wave I know.

Now if someone could give me a real life analogy of a spinor wave my life will be complete :).