# School me on gravity waves

1. Aug 18, 2011

### mrspeedybob

From my internet research I gather that they are very hard to detect but is that because the energy carried by the waves is so tiny or because it is hard to get that type of energy to interact with an instrument in a measurable way?

Do gravity waves, as a form of energy, have their own gravitational field? That is to say, if a gravity wave passed close to a stationary object would it be deflected and would it alter the velocity of the object, like light waves are and do?

Is the speed of a gravity wave c in all reference frames?

What about gravity waves that are high in frequency but low in amplitude such as those that would be generated by an atom as it moves about due to its thermal energy? I would assume that the energy carried by a gravity wave would depend on both amplitude and frequency. Is there any research being done in this area?

2. Aug 18, 2011

### WannabeNewton

The gravitational wave solutions to the linearized EFEs have very low amplitudes so yes they do not interact strongly. If you take the energy flux across a plane of harmonic oscillators you will see that the energy loss for the gravitational wave is so little that the damped harmonic oscillator solution will barely be affected.
The effect of gravitational waves in the linearized GR is straightforward. Take a plane wave traveling in the +z direction that is + polarized: if you start with particles arranged in a ring initially at rest then
$$\frac{D^{2}\xi ^{\alpha }}{D\tau ^{2}} \approx \frac{\partial ^{2}\xi ^{\alpha }}{\partial t^{2}} = R^{\alpha }_{0 0 \nu }\xi ^{\nu }_{(0)}$$ and from this you figure out that $$\frac{\partial^2 \xi ^{x}}{\partial t^2} = -\frac{\partial^2 \xi ^{y}}{\partial t^2}$$ While this isn't concrete enough to see the result, basically what happens is that the ring of particles is stretched into an ellipse with the major and minor axes varying periodically as the wave passes through. Just solve the geodesic equation with the related components of the linearized riemann tensor inputted and you will find that you can take the x and y solutions and get the equation of an ellipse.
Within the linearized EFEs, yes. Consider the plane gravitational wave $\bar{h_{\mu \nu }} = A_{\mu \nu }e^{ik_{\alpha }x^{\alpha }}$. Then, $$\square ^{2}\bar{h_{\mu \nu }} = \partial ^{2}_{t}\bar{h_{\mu \nu }} - c^{2}\triangledown ^{2}\bar{h_{\mu \nu }} = \omega ^{2} - c^{2}\left | k \right |^{2} = 0$$ so $\frac{\omega }{\left | k \right |} = c$ for all.

3. Aug 19, 2011

### Passionflower

If we use Post-Newtonian approximations gravity waves are really (mathematical) waves, but I have doubts if the term 'wave' is truly the best way to characterize what is going on.

Instead of waves I would prefer to think of 'changes to the gravitational field in time'.

4. Aug 19, 2011

### rbj

i might suggest to maybe check out http://en.wikipedia.org/wiki/Gravitomagnetism . i think the title should be Gravitoelectromagnetism (or GEM).

i have a sorta simplistic view: static EM is inverse-square and propagates at the speed of c. also the classical magnetic interaction is nothing more than the electrostatic interaction but with special relativity taken into consideration.

gravity is inverse-square and, according to principles in General Relativity, propagates at the same speed of c. then the question to ask is: "do moving mass charges create, from the POV of classical physics, the same kind of interaction we call "magnetism" for the EM case?"

i can't do the math, but it turns out that the Einstein Field Equation can, assuming speeds much slower than c and reasonably flat space-time (like we're not hanging around a black hole) sorta degenerate to something that looks like Maxwell's Equations for EM. then gravity waves happen from solving the same kind of equations that EM wave come from.

5. Aug 19, 2011

### jnorman

seems to me that in order for a gravity wave to be detectable, the center of gravity of a massive object would have ot be displaced to such an extent that it would have an effect on other objects. not an easy feat. even a super giant going nova would not alter the COG of the star's overall mass and would not be noticeable at any distance.

i really dont know of any way to significantly affect COG of any truly massive body, other than perhaps galaxies colliding. i am insufficiently schooled on why researchers think they might detect gravity waves from any sources within our galaxy.

6. Aug 19, 2011

### Bill_K

The center of mass is not involved. Gravitational waves are quadrupole and higher. All a massive body has to do to generate gravitational waves is sit still and vibrate.

7. Aug 19, 2011

### jnorman

thanks bill - can you please elaborate on why the quadrupole aspect elevates probability of detection?

8. Aug 19, 2011

### DrGreg

Re: School me on gravitational waves...

The Wikipedia article Gravitational wave contains an animation that illustrates the effect a gravitational wave can have on matter.

Technicality: a gravity wave is not the same thing as a gravitational wave.

9. Aug 19, 2011

### pervect

Staff Emeritus
The commonly expected sources of gravity waves that we hope to measure are those from rotating gravitational collapse and rotating inspirals.

Gravitational collapse to a black hole is by far the "loudest" source for gravity waves, it's much better at generating them than any explosion. In fact, a spherically symmetric (and non-rotating) explosion wouldn't generate any gravity waves at all.

Note that we can detect the loss of energy indirectly for the one binary pulsar we've found - we don't directly detect the gravity waves from it, but we can predict and measure the rate of inspiral and associate it with a loss of energy. This is almost as straightforwards as it sounds, while GR doesn't have a truly global concept of energy, the situation is symmetrical enough that there are some definitions that apply.

In theory any rotating nonspherical object should generate gravity waves, but they are way too weak to measure. For instance, MTW has some textbook calculations for a steel beam, rotating as fast as it can without being torn apart, the numbers are tiny! (I'd have to look them up to quote the exact values).

10. Aug 21, 2011

### mrspeedybob

Thank you all. I have some research to do before I will understand some of these answers but at least I know what I need to research.

Since no one mentioned it I presume that no one knows of any research on gravity waves from microscopic sources such as vibrating atoms. Would this be a question to pose to the LQG guys in the "Beyond the standard model" section or is it something that is completely unstudied as of yet?

11. Aug 21, 2011

### pervect

Staff Emeritus
I'm not sure of your interest,but since we can't measure the gravity waves from much more massive objects than atoms, and we more or less expect the amplitude to depend on mass, so that massive objects would be a much better source, it seems not particularly fruitful to ask what happens with atoms, at least to me.

12. Aug 21, 2011

### mrspeedybob

The thought was that since the energy of a wave depends on both amplitude and frequency a high frequency, low amplitude wave, such as from a vibrating atom may contain more energy then the mass of the atom would suggest. Since the big bang a lot of atoms have been doing a lot of vibrating. In the dense soup of particles immediately after the big bang there was a tremendous amount of heat. If every particle that has ever accelerated has radiated gravity waves that would be a considerable amount of energy. Where is all that energy now? Is it still propagating through the universe as tiny, undetectable, high frequency gravity waves? If so, could it be responsible for some of the seemingly random behavior of quantum particles? Could it be a portion of the dark matter or dark energy content of the universe?

I'm trying to learn enough to make some quantitative study of this so I can at least make an educated guess about the answerers to these questions, unless someone else has done so before, in which case I'm curious what they found.