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There are a lot of questions and answers on this site about light traveling in straight lines in vacuum (following a geodesic). And there are a lot about both EM and gravitational waves traveling at the same speed $c$.

I have read this question:

When we look at light propagating in the classical limit then it travels in straight lines.

How do single photons travel from here to there

And this one:

the gravitational wave paths are the same as light paths

Do gravitational lenses work on gravitational waves?

Now based on these, gravitational waves should always travel in a straight path (follow geodesics), just like EM waves. Actually, this is what we call a null geodesic.

Why is light described by a null geodesic?

But is this correct, that gravitational waves must travel in straight lines always, following null geodesics, and can this be proven?

As per the comment, the question is more interesting, because geodesics follow the curvature of spacetime, and gravitational waves are perturbations of spacetime itself.

Question:

  1. Do gravitational waves travel always in a straight line (along a geodesic) like EM waves?
Árpád Szendrei
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  • Do you mean to ask this only in relativity models? That is, you're not referring to an EM wave as described by classical electrodynamics? – Daddy Kropotkin Jan 03 '21 at 18:17
  • This is a more subtle question than you may think. Do Airy beams travel in straight lines? So even light does not quite travel in straight line. Plane-waves do, but you can come up with rather exotic configurations of electromagnetic field that will surprise you :-) – Cryo Jan 03 '21 at 22:58
  • @DaddyKropotkin yes, classical is fine. – Árpád Szendrei Jan 04 '21 at 00:58
  • I think the question the poster is asking is "do gravitational waves travel along geodesics?". Which is a very interesting question, since geodesics are defined by the warping of space-time, and gravitational waves are a warping of space-time... – ZenFox42 Jan 04 '21 at 13:42
  • @ZenFox42 thank you I edited the question. – Árpád Szendrei Jan 04 '21 at 16:38
  • It's important to remember, both for light and for gravitational waves, that this result is based on the approximation that the intensity of the wave is small enough that it does not change the background spacetime. This question seems to be kind of asking "doesn't the gravitational wave interact with the underlying spacetime", and the answer is "yes", but the second that the wave is large enough that the interactions are detectible, the answer becomes "everything gets really, really complicated, and coming up with general behaviour is hard" – Zo the Relativist Jan 04 '21 at 16:52
  • @JerrySchirmer thank you, do I understand correctly, that you are saying, that the current GWs we can detect, do change the background spacetime, that is, they change the very geodesic they move along too (temporarily of course)? – Árpád Szendrei Jan 04 '21 at 17:00
  • @ÁrpádSzendrei, Yes, but the effect is so extremely small that it cannot be measured, because the gravitational waves are already so small to be at the extreme edge of detectability, and any interaction with the background would be a second order effect, and smaller still. – Zo the Relativist Jan 04 '21 at 19:55
  • @JerrySchirmer I understand, so if it is so small, then if we disregard it, do you think GWs are moving along geodesics (like EM waves)? – Árpád Szendrei Jan 04 '21 at 19:57
  • @ÁrpádSzendrei yes. This is a derived result that can be obtained as an "exact" result in the limit that the GW wave interactions are small. – Zo the Relativist Jan 05 '21 at 16:49
  • @JerrySchirmer seems like an answer. Would you like to write it up? – Árpád Szendrei Jan 05 '21 at 17:06

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In this link the similarities and differences of gravitational waves to electromagnetic waves is explored .

You ask:

Do gravitational waves travel always in a straight line like EM waves?

I think that the straight lines are the light ray description of light ,

In optics a ray is an idealized model of light, obtained by choosing a line that is perpendicular to the wavefronts of the actual light

There are equivalent rays defined for gravitational waves and that is the geometric optics, which when wavelengths become too large for the system studied have to be modified, as this link suggests.

It is standard practice to study the lensing of gravitational waves (GW) using the geometric optics regime. However, in many astrophysical configurations this regime breaks down as the wavelength becomes comparable to the Schwarzschild radius of the lens.

There is also this link:

The geometrical-optics expansion reduces the problem of solving wave equations to one of the solving transport equations along rays. Here, we consider scalar, electromagnetic and gravitational waves propagating on a curved spacetime in general relativity. We show that each is governed by a wave equation with the same principal part. It follows that: each wave propagates at the speed of light along rays (null generators of hypersurfaces of constant phase) ......

Glorfindel
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anna v
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the gravitational wave paths are the same as light paths

I cannot agree with this quote.

Light or more generally EM radiation consists of photons. These quanta do not dissipate from their beginning (emission) to their end (absorption). A photon beam from a laser, for example, is limited in diameter and the focus is not so perfect that this diameter will remain constant.
The diameter of the light beam increases over distance, but the gravitational potential as a kind of medium has (almost) nothing to do with it. The energy content of the quanta does not change, the number of quanta does not change and they do not dissipate along their geodesic path.

The same cannot be said about the gravitational potential. Whether expressed by gravitons or not, the gravitational potential above the scale of gravitons is a continuum. A mountain on a celestial body will never result in a discontinuity for a spacecraft orbiting such a body. It follows that gravity is dissipative in space.

HolgerFiedler
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