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A very layman question as in title. Like every wave having a negative side, can a gravitational wave have anti-gravity.

To put it in different words, a gravitational wave passing through a complete vacuum, if in positive cycle, can create a denser space-time, in it's negative cycle, create a rarer space-time?

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    $\begingroup$ There is no positive and negative cycle. It expands in one direction and compresses in the other, to make a circle turn into an ellipsoidal, and oscillate back and forth where it then reverses and contracts in one direction and expands in the other. The volume does not change. Space like slices in spacetime in GR can have varying curvatures. The wave having positive sides and negative is simply your visualization, and in the two dimensions minimum to visualize gravitational waves not useful. Similarly to EM waves, the motion induced is not along the direction of the wave, but perpendicular. $\endgroup$ – Bob Bee Aug 17 '16 at 4:48
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Gravitational waves, though transverse, can be thought of as similar to sound waves:

A sound wave, as it moves through a medium the sound wave creates alternating volumes of greater and lesser particle density.

Gravitational waves do something similar, except the medium is spacetime itself. The result is that as a gravitational wave passes through a region of space, at one crest the spacetime is "stretched" in one direction and contracted in the perpendicular direction, like when you stretch a rubber band and it gets narrower. At the trough of the wave, the same thing happens, except the direction that was contracted is now stretched and the direction that was stretch is now contracted. This is why the good ol' perpendicular lasers and mirrors trick worked for detecting them.

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    $\begingroup$ I think sound waves are longitudinal. You've thought probably on the EM waves. $\endgroup$ – peterh Aug 16 '16 at 22:07
  • $\begingroup$ #2: As I know, the gravitational waves don't change the volume they travel. $\endgroup$ – peterh Aug 16 '16 at 22:10
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    $\begingroup$ They can propagate as transverse waves in solids, and the compression/expansion part of sound waves is what I use as an analog for the action of a gravitational wave. I'll change it for better accuracy. $\endgroup$ – hebetudinous Aug 16 '16 at 22:10
  • $\begingroup$ I know the volume doesn't change; the spacetime is just distorted. The contraction in the orthogonal direction cancels out the increase in volume that the stretching would cause, I think. $\endgroup$ – hebetudinous Aug 16 '16 at 22:13
  • $\begingroup$ The analogy with sound waves isn't very good. Actually, the main thing the OP seems to need is an explanation of the fact that the analogy with sound waves isn't valid. A this doesn't answer the question about attraction and repulsion. $\endgroup$ – user4552 Apr 17 '19 at 14:03
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Gravitational waves are not cycles of compression and rarefication like sound waves. They're transverse, and there is no such thing as compression or expansion of spacetime. There is curvature of spacetime. In a gravitational wave, the curvature is what oscillates.

In general relativity, the precise definition of what we mean by attractive or repulsive gravity is complicated, and difficult to express without some mathematics. We express this definition in a set of various criteria called energy conditions. The energy conditions are all automatically obeyed in a vacuum, so gravitational waves do not contain repulsive gravity.

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Gravity is always attractive as it creates a positive curvature in spacetime. Then, such curvature in the 4D hypersurface is like "a mesh" of geodesics. These geodesics are the path you follow in a free fall when attracted by another massive body nearby, made of positive mass. The local curvature of the 4D hypersurface is then locally positive (spherical geometry), and the geodesics always evoke gravitational attraction.

If one could generate a negative curvature in spacetime, either by producing some exotic matter of negative mass, or by concentrating enough negative energy density locally (neither is known), then a negative curvature would be induced in spacetime, a hyperbolic geometry (or horse saddle geometry) producing geodesics and a free-fall path that evoke gravitational repulsion, i.e. antigravity.

As for the gravitational waves, they have indeed been detected (by LIGO/Virgo), but their associated quantum that would mediate gravity, a 2-spin boson called the "graviton", is still hypothetical and AWOL for a century. Not all fields have a mediate elementary particle. Gravitational waves could just be "ripples in spacetime", like 2D ripples on the water surface of a pond. Einstein's coupling constant 8πG/c⁴ in his field equations tells us how is such "coupling" i.e. the direct relation between how much spacetime is distorted (the Gμν tensor, LHS) with respect to the amount of local matter-energy (Tμν tensor, RHS). It shows the stiffness of spacetime and how it is extremely rigid: indeed, the coupling constant has the light speed raised to the fourth power at the denominator, making it extremely small.

So any gravitational waves are very tiny, even with a lot of energy focused locally, so any gravitational waves that would be artificially produced in the future are expected to be very weak. It is no coincidence that such waves have been detected thanks to the gigantic energy released by the merging of two black holes, yet the signal was almost lost in the noise and its detection required a particularly elaborate algorithm.

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    $\begingroup$ Note that we do have MathJax enabled on this site, so you can get LaTeX-like equations by wrapping your equations in the dollar signs. Search notation in help center more. $\endgroup$ – Kyle Kanos Apr 17 '19 at 11:45
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    $\begingroup$ This doesn't answer the question, and the discussion of the physics is not really right. It doesn't make sense to say that the coupling constant measures the stiffness of space or that its numerical value is small. Small compared to what? This depends completely on the system of units being used. $\endgroup$ – user4552 Apr 17 '19 at 14:05
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So it looks:

So it looks

Some more details:

  • The GWs are transverse waves, not longitudinal ones
  • Gravity is not a force in the GR
  • They don't produce "anti-gravity", i.e. their effect isn't in an opposite direction to the source, it is perprendicular to them
  • Also the GWs don't produce a force, they change the metric in the space they travel. As this change shrinks in a direction, it grows in the other, thus the volume they travel doesn't change. Like so (source):

enter image description here

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  • $\begingroup$ Gravitational waves are transverse waves just like electromagnetic ones, and light absorbing on an object will provide a repulsion effect. $\endgroup$ – Tom Andersen Aug 17 '16 at 1:06
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    $\begingroup$ @Tom That is not a repulsion, see my comment in your answer. It is simply momentum transfer from the wave to the body or viceversa, as I related above. The wave itself, and in both cases it could be the identical wave, will still have an attracting effect on anything due to its mass. In GR, it is not possible to have a negative mass. The gravitational wave case is even simpler, it's a linear approximation, and you can treat it as a field just like EM, except spin 2. Spin 2 particles, I.e., gravitons, can only attract, there can't be two opposite 'charges'. You are way off in your thinking. $\endgroup$ – Bob Bee Aug 17 '16 at 4:36
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    $\begingroup$ @TomAndersen "Gravitational waves are transverse waves just like electromagnetic ones" <- this is also what I wrote. "light absorbing on an object will provide a repulsion effect" <- I didn't even mention light in any sense. I am sorry, but it doesn't seem, you had understood this sub-high school level text, or you had even read it. $\endgroup$ – peterh Aug 17 '16 at 5:55
  • $\begingroup$ Bob - gravitational waves are not a 'linear approximation'. Yes weak ones can be very well modelled by a linear approximation, but waves can be be very much in the non linear regime. Please note the question - which was not about negative mass, but rather if gravitational waves can create a repulsive effect, which they certainly can. The transverse nature of the waves has nothing to do with attraction or repulsion. $\endgroup$ – Tom Andersen Aug 17 '16 at 22:55
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    $\begingroup$ @TomAndersen The question was about the experimentally detectable waves. Yes, they are linear. Read this. May I ask you, what is your real problem? $\endgroup$ – peterh Aug 18 '16 at 6:13
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I will re-form your question by ignoring the second and third sentence, which are not too clear.

Can gravitational wave create anti-gravity, i.e. repulsive gravity?

Yes.

Its the same as for light: if light - which carries momentum - is absorbed by an object then that object moves away from the light source.

The trick with gravitational waves is that normal matter does not absorb gravitational waves very well. (But there is always some absorption).

To Maximize the Effect:

If gravitational waves impinge on any rotating object there can be repulsion or attraction. The effect is only really strong when waves impinge on a rapidly rotating compact object like a spinning black hole. To get a nice large effect the period of the waves need to be of the same size as the spin rate.

The effect when its an near coherence mode is called super radiance.

For repulsion the effect is actually an absorption of gravitational energy from the wave, so that the object starts to move in the same direction as the wave. See Figure 16 of Brito: - http://arxiv.org/pdf/1501.06570v3.pdf

The effect can be quite pronounced. 10% of the incoming energy of the wave can be absorbed.

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    $\begingroup$ That is not antigravity, it is simply transfer of momentum from the wave to the body. It is similar to when a body (such as in the end stages of black hole mergers) emits gravitational radiation, the body as a recoil momentum in the direction opposite the radiation. If both cases, it is simply momentum being absorbed or sent out in the gravitational waves. The waves are the same except for parameters like freq, polarization, power, and so on. Apart from those effects, which are momentum conservation, the wave has energy and effective gravitational mass, and attracts all other objects. $\endgroup$ – Bob Bee Aug 17 '16 at 4:10
  • $\begingroup$ Gravitational waves are transversal, and thus their effect is never to move the object away from the source. $\endgroup$ – peterh Aug 17 '16 at 5:58
  • $\begingroup$ Peter H. Electromagnetic waves are also transverse, yet they produce radiation pressure, moving the object away from the source. The only reason why large wavelength gravitational waves have only a feeble push effect on ordinary matter is that they don't interact much with things like the earth. $\endgroup$ – Tom Andersen Aug 17 '16 at 22:46
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    $\begingroup$ Bob - it would sure feel like antigravity! You are using gravitational interactions to force objects apart. I agree with your comment, and it sums up pretty well my answer as well. $\endgroup$ – Tom Andersen Aug 17 '16 at 22:49
  • $\begingroup$ Momentum transfer IS repulsion. That's how QED, etc models repulsion in static Coulomb fields. If you look at how radiation pressure works its exactly the same as static EM repulsion - there is momentum transfer. $\endgroup$ – Tom Andersen Aug 17 '16 at 22:58

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