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I heard that gravitational wave is the measure of stretchiness of space time, so since there is no limit to how fast space can stretch what about gravitational wave?

Qmechanic
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user6760
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    The wave would be essentially "frozen" on the quickly expanding background. Locally nothing particularly exciting happens. – CuriousOne Mar 25 '16 at 01:53
  • Pretty sure those are different kinds of stretching. The one you're talking about is a vibration stretch, which stretches an object back and forth, with no permanent expansion. The 2nd is a property of space, which expands but doesn't expand objects cause they're bound, only the space between objects expands. – userLTK Mar 25 '16 at 02:16

2 Answers2

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There is an existing mathematical model of astrophysical observations which used in the Big Bang model fits the observations well. This model is based on general relativity and in General Relativity the velocity of light as c is inherent in the equations and thus also in the derivation of gravitational waves.

The speed of gravitational waves in the general theory of relativity is equal to the speed of light in vacuum, c.1 Within the theory of special relativity, the constant c is not exclusively about light; instead it is the highest possible speed for any interaction in nature. Formally, c is a conversion factor for changing the unit of time to the unit of space.2 This makes it the only speed which does not depend either on the motion of an observer or a source of light and/or gravity. Thus, the speed of "light" is also the speed of gravitational waves and any other massless particle.

This is so by construction of the mathematics.

Until the recent LIGO experimental findings gravitational waves were just a hypothesis, and now one sees data that fit this hypothesis. At present the expansion of space is modeled within General Relativity, and this expansion does not affect the velocity of propagation in the solutions of the wave equations, by construction. What it does affect is the wavelength, as happens also with the electromagnetic radiation which by the redshift effect has given us the data for the expansion of the universe.

A gravitational wave will get a larger and larger wavelength as it propagates on an expanding space, itself with velocity c.

The gravitational wave is an oscillatory disturbance on the stress energy tensor that propagates from where energy and mass are concentrated as a distortion of space time. The expansion of space is an independent change of the metric of space due to the cosmological constant or , for accelerating expansion, other mechanisms under research. Both the electromagnetic waves and the gravitational waves propagate on the space time but are not generating it, (except as tiny perturbations due to the energy they carry).

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anna v
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  • Anna's answer gets my vote on 'the answer'. With a couple of unimportant statement changes. – Bob Bee Mar 27 '16 at 03:44
  • The two small changes are: 1) grav waves don't have a stress energy tensor, really it is a pseudo tensor that one can separate from the empty spacetime G mu, nu. And interpret as the stress tensor of the grav waves which are 'vibrating. 2) the speed is c not because of mathematical constructs. In EM it comes from Maxwell equations, and led Einstein to construct SR when it was shown by Michelson Morley that it was the same for any observers moving at a constant v with respect to the other. Since GR must reduce to SR for flat spacetime, c was also then part of GR. Physical reasons, not math – Bob Bee Mar 27 '16 at 04:01
  • @BobBee on your 2) there might have been another model, where special relativity appears at flat spacetime but curved has a different behavior, no? the simplest is this choice of course. – anna v Mar 27 '16 at 04:06
  • sorry just saw this. Well, GR had to reduce locally to SR, everywhere, so hard to see how it could be c locally in GR, and change when you change coordinates. C (in GR) would then have had to a non-scalar field of some sort that in local inertial coordinates was the constant c? Not sure I can envision it? Wonder if in some way it'd be equivalent to taking c as constant and introducing some other field, not sure what kind of field. – Bob Bee Apr 20 '16 at 05:17
  • More. In reality it has to be some simple logical consistency that is requires it, too much of a coincidence if not. So I'm betting it can be proven, by having it reduce locally to c. I'm just not getting to that proof. – Bob Bee Apr 20 '16 at 05:22
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Assuming space really stretches and say it does so at Faster Than Light -

The gravitational wave in an FTL-stretching space would lose its amplitude as the wave itself will stretch with space. Wave is space, it is not an object (bound) so it will stretch with space. Its wavelength will also increase at the same time.

Therefore, part wave will travel/stretch at FTL, but not due to the wave nature, but only due to stretching space. Soon it would lose all the amplitude and spread too thin to be called a wave anymore.

Now, can we use presence of gravitational wave as an evidence that space is not stretching at FTL? Because, if it were, then the GW in a stretching space would die soon.

SuperCiocia
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