Do gravity waves get bent by gravity?

Main Question or Discussion Point

do gravity waves die under own gravity?

do gravity waves get distorted passing gravitational sources? i assume they must do, but gravity itself does not. if so their calculations must get extremely complex extremely quickly when waves interact with each other AND gravity itself. if so, wouldnt gravity waves fall aprt under their own gravity, as peaks travelled slower than troughs, due to higher temporal distortion on peaks?

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pervect
Staff Emeritus
jim_990 said:
do gravity waves get distorted passing gravitational sources? i assume they must do, but gravity itself does not. if so their calculations must get extremely complex extremely quickly when waves interact with each other AND gravity itself. if so, wouldnt gravity waves fall aprt under their own gravity, as peaks travelled slower than troughs?
Gravity waves do get "bent by gravity" - in the sense that they follow the same geodesics that light does, at least in the limiting case where both the gravity waves and the light beams are "weak" so that they don't affect the local metric.

Gravity waves are almost always analyzed in the linearized theory, where it is assumed that the intensity of the gravity wave is low. I should note that this is a very good approximation, the intensity of the waves is so low that we haven't been able to sucessfully measure one yet. Thus the effect of gravity waves on themselves is tiny under normal circumstances, and is usually ignored.

Calculations of strong gravity waves including the nonlinear effects would indeed be complicated. The nonlinearity of gravity is what makes General Relativity a considerably more complicated theory than the relativistic theory of electromagnetic radiation (relativistic electrodynamics).

Calculation of the non-linear effects on weak waves should be possible, but I'm not familiar with it. Offhand, I'd expect normal effects of small non-linearites - small amounts of "mixing" of different frequencies, and the generation of higher order harmonics. The beahvior of radio waves or optics in the presence of non-linear media would serve as a reasonable guide of the sorts of effects to expect.

Since we currently haven't even been able to detect gravity waves, detecting any such hypothetical effects is a long way off - we can expect that they are basically insignificant in any practical terms.

Stingray
For details, I think that there is a book by Chandrasekhar regarding gravitational waves propagating in strongly curved backgrounds, colliding waves, etc.

Chronos
Gold Member
A very interesting idea in gravity wave propogation is the notion of constructive interference between gravity waves.

jim_990 said:
do gravity waves get distorted passing gravitational sources?
Yes.
i assume they must do, but gravity itself does not. if so their calculations must get extremely complex extremely quickly when waves interact with each other AND gravity itself.
Actually yes it does, but you are right that it complexifies the equations. They are nonlinear and so superposition does not work for general strong fields. This is why there are so few exact solutions to Einstein's field equations.
if so, wouldnt gravity waves fall aprt under their own gravity, as peaks travelled slower than troughs?
I'm not sure why you infer that, but analysing strong gravitational waves isn't as simple as multiplying the weak field solutions by an amplitude factor.

gravity waves falling apart under their own gravity:- in most cases even in troughs the level of gravity would be high, just higher on peaks, ie in the case of a mountain on a rotating planet, where we would not have a wave that dropped to zero in troughs, but just dropped a little bit. But in any case, the peaks should slow themselves down more than the troughs, until over a long enough distance or with a big enough amplitude and/or short enough wave lengths, the whole wave would become flat & unmeasurable

the wave would create a wave like temporal gradient travelling with the gravity wave, which should cause peaks to lag, so only long wavelengths with small amplitudes would travel long distances without some sort of skew.

pervect
Staff Emeritus
In an asymptotically flat space-time, gravity waves could not disappear, because there is no place for their momentum and energy to go. Gravitational interaction would simply distort the wave into some non-sinusoidal shape.

In a non-flat space-time, these remarks don't apply. Gravity waves (weak or strong), would undoubtedly experience a cosmological red-shift just like light does.

Chronos
Gold Member
Conservation of energy rules, although I would not limit it to the case of asymptotically flat spacetime. I think you should be able to recover energy conservancy under any metric. That does not mean pervect's example is flawed. He is merely pointing out it has been mathematically confirmed for that particular model.

pervect
Staff Emeritus
There's a very slim chance that I'll change my tune, if the gravity probe B results turn out to support (for instance) Garth's theory (SCC) rather than General Relativity.

Meanwhile, I have to go with GR. The status of energy conservation in GR is reasonably well spelled out in the sci.physics.faq on the topic

http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

gravity waves' troughs are positive & their peaks, im not saying any energy is lost, all im saying is that the peaks and troughs blend into a mean flat line halfway between the 2, as the peaks get stretched backwards into the troughs.

ie during a peak, the wave tries to redshift more than in a trough due to the temporal distortion being higher in the peak

how is it possible to detect a gravity wave? If we exist in a world which can be compressed and stretched with everything inside maintaining the same proportions, we shouldn't be able to detect anything. I'm thinking of 'flatlanders' when I'm writing this, and since there is no way for a flatlander to detect a bend in their 2d world, then there shouldn't be any way to detect a bend in our 3d world. If you have a really long experiment with a laser shining down the whole thing, theoretically when the gravity wave passes by, it will strike one end first (provided it's direction of travel is in line with the length of the detecting laser) and contract it while the other side remains the same as before. Supposedly this is going to enable us to detect it, but isn't the light within the beam also contracted along with everything else (since it is bound to space-time just like matter is) thus making it impossible to detect a wave? If there is a fold in space-time, doesn't light get folded too, so that if you are looking into space-time that is folded, it still looks like you are looking straight ahead?

if space contracts, whats in it contracts too! it may not be noticable! Also bear in mind temporal changes, if they are not uniform, which they are not, as the effect dies with distance, your detector will detect it. Whether gravity waves exist or not is the real question. Your theory is right in some respects, but not fully sound, we are not trying to measure a global change, but waves, which make local changes and so these detectors will be out of sync