Talk:Gravitational wave

Suggested addition: Einstein’s original derivations and historical foundations

Hello, I would like to propose adding a scholarly reference that directly addresses and reconstructs the content described in the article’s section on Einstein’s 1916 gravitational wave paper.

The Wikipedia article currently summarizes Einstein’s 1916 paper as the outcome of efforts to reconcile the absence of negative gravitational charges with wave generation in general relativity, culminating in his June 1916 publication. However, the mathematical and conceptual structure of that paper—and its follow-up in 1918—has not been thoroughly analyzed in the current literature referenced here.

The book Einstein’s Legacy: From General Relativity to Black Hole Mysteries by Galina Weinstein (Springer Nature, 2025) provides a line-by-line reconstruction and analysis of both Einstein’s 1916 and 1918 gravitational wave papers. It explores Einstein’s derivation steps, interpretation of the three wave types (as later characterized by Weyl), and the key approximations he used. The book also connects these methods to later applications. For example, it demonstrates how Hans Thirring and Josef Lense employed Einstein’s approximation techniques to analyze rotating systems in 1918, decades before the Kerr solution was established.

Reference: Weinstein, Galina. Einstein’s Legacy: From General Relativity to Black Hole Mysteries. Springer Nature, 2025. https://link.springer.com/book/10.1007/978-3-031-73572-1

Please let me know if this contribution would be suitable for enriching the article’s historical development section, particularly the paragraph discussing the 1916 and 1918 gravitational wave models. Best regards, Contributor Dg1702 (talk) Contributor Dg1702 (talk) 07:34, 13 July 2025 (UTC)

Sounds awesome (if it doesn't unbalance the section). Johnjbarton (talk) 18:26, 13 July 2025 (UTC)

Thank you, Johnjbarton! I appreciate your encouraging feedback. I’ve revised the contribution to keep it concise and aligned with the tone and balance of the current section. I suggest inserting the following sentence directly after: “The result was published in June 1916,[4] and there he came to the conclusion that the gravitational wave must propagate with the speed of light.”

A detailed reconstruction of the derivations and mathematical structure of Einstein’s 1916 and 1918 gravitational wave papers appears in Einstein’s Legacy: From General Relativity to Black Hole Mysteries (2025) by Galina Weinstein. The book presents a line-by-line analysis of Einstein’s approximation methods, his formulation of the wave types later characterized by Weyl, and the underlying physical assumptions. It also connects these derivations to subsequent work by Hans Thirring and Josef Lense, who used Einstein’s linearized field equations to analyze rotating systems—decades before the development of the Kerr solution for rotating black holes.^[X]

With the citation:

[X] Weinstein, Galina. Einstein’s Legacy: From General Relativity to Black Hole Mysteries. Springer Nature, 2025. https://link.springer.com/book/10.1007/978-3-031-73572-1

Please let me know if this phrasing fits well or if any fine-tuning is needed before proceeding further. Dg1702 (talk) 19:29, 13 July 2025 (UTC)

Sorry, but I don't think this approach fits with wikipedia science articles. In fact I would argue that this strategy is inappropriate. By reporting on what Galina Weinstein wrote ("A detailed reconstruction...") you are effectively analyzing Weinstein. Rather we need to treat Weinstein as the analyst and summarize what the author says about Einstein's treatment of waves and cite the book. HTH. Johnjbarton (talk) 21:45, 13 July 2025 (UTC)

Thank you, Johnjbarton — I understand your point now and appreciate the clarification. Instead of suggesting a new paragraph, I’d like to propose a more minimal edit:

I suggest simply adding a citation to the book at the end of the following sentence in the History section:

“The result was published in June 1916,[4] and there he came to the conclusion that the gravitational wave must propagate with the speed of light, and there must, in fact, be three types of gravitational waves dubbed longitudinal–longitudinal, transverse–longitudinal, and transverse–transverse by Hermann Weyl.[27]”

The book provides historical and mathematical commentary on this exact derivation and the identification of the three wave types:

Weinstein, Galina. Einstein’s Legacy: From General Relativity to Black Hole Mysteries. Springer Nature, 2025. https://link.springer.com/book/10.1007/978-3-031-73572-1

Please let me know if this citation is acceptable. Dg1702 (talk) 06:07, 14 July 2025 (UTC)

Please go ahead. I will make adjustments. Thanks! Johnjbarton (talk) 22:57, 14 July 2025 (UTC)

Gravitational Standing Waves

I've already suggested this on the wikipedia article for standing waves, and I think it might be a potentially good thing to add to this article as well.

The hypothetical phenomenon of gravitational waves propagating in opposite directions and superimposing to form spacetime distortion oscillations is currently theoretical (and will likely continue being that way considering the sheer unlikeliness of ever observing such an occurence) and perplexingly complicated mathematically, but the concept has definitely been pioneered in theoretical physics oriented around General Relativity.

I'd thus propose adding a brief section covering this niche, though fascinating, idea. Xyqorophibian (talk) 13:55, 29 September 2025 (UTC)

The proper citation would be

• Szybka, S. J., & Cieślik, A. (2019). Standing waves in general relativity. Physical Review D, 100(6), 064025.

However, as far as I can tell the only citations for this work is by the authors themselves. I don't think this makes the content notable. Johnjbarton (talk) 18:56, 29 September 2025 (UTC)

Hello Johnjbarton.

Thank you for the specifying citation conventions and notability policies of Wikipedia.

As for your first sentence, I'm confused (I am not an author of that paper).

Though after further research I sorta agree that there's probably not enough about this particular topic for much to be written about it.

Your reply is appreciated.

Xyqorophibian (talk) 00:22, 30 September 2025 (UTC)

? I guess by first sentence you meant "...only citations for this work is by the authors themselves."? If you look at the citations on Google Scholar, there are 10, but only one that is published and not by Szybka. That is what I meant by not yet notable. Johnjbarton (talk) 01:20, 30 September 2025 (UTC)

Oh, right.

I apologise for the misunderstanding. Xyqorophibian (talk) 01:38, 30 September 2025 (UTC)

Misleading and Inaccurate Definition

The definition of gravitational waves in this Wikipedia article,

Gravitational waves are oscillations of the gravitational field that travel through space at the speed of light; they are generated by the relative motion of gravitating masses

, is not completely correct.

First off, describing them as oscillations implies they exhibit some kind of periodicity (i.e. not necessarily even perfect repetition, but just at least some constant frequency) and this is already a contradiction considering that waves (including gravitational waves) can be aperiodic (i.e. have no single constant rate at which they cause oscillations). And even aside from that, thinking of waves as travelling oscillations is a misconception (instead, they are propagating dynamic disturbances that can cause oscillations).

Secondly, defining gravitational waves as being a phenomenon occurring in gravitational fields is just wrong as the idea of a gravitational wave originates from General Relativity (which doesn't use gravitational fields to describe gravitational interactions between masses), not the gravitational field - oriented Classical Mechanics (which doesn't predict gravitational waves at all).

Lastly, this a subtle/minor difference but wouldn't it be better to say that they travel through spacetime rather than space itself?

Other than that, the other details are fine.

I'd suggest changing the definition to being something like this:

A gravitational wave is a wave of spacetime distortion/curvature that propagates at the speed of light and is produced by the relative motion of gravitating masses.

I know, still not perfect (e.g. doesn't specify that motion as a source must lead to a time-varying quadruple moment of mass distribution) but it's still more accurate in a technical sense than the current one. Of course there's always points for refinement, like obviously distortion/curvature could be linked to the mathematics behind General Relativity.

Hope this will serve as a potential improvement, no (destructive) criticism intended. Xyqorophibian (talk) 01:33, 30 September 2025 (UTC)

I agree with your criticism. To make the case for the alternative we need some secondary sources.

One choice would be page 561

• Zee, Anthony (2013). Einstein Gravity in a Nutshell. In a Nutshell Series (1 ed.). Princeton: Princeton University Press. ISBN 978-0-691-14558-7.
• "...Einstein's gravity predicts the existence of ripples crisscrossing the fabric of spacetime..."

Johnjbarton (talk) 02:41, 30 September 2025 (UTC)

Hello @Johnjbarton,

Thank you for your acknowledgement of my points and your agreeance with my definition.

I'll edit the gravitational wave definition on this article to my alternative version, though I'm afraid I won't be able to do much with those sources because I am unfamiliar with citations & referencing as an inexperienced Wikipedian.

Glad this has helped out somehow, though I entirely expect corrections and refinements to be made (after all it can still improve). Xyqorophibian (talk) 04:20, 30 September 2025 (UTC)

I'm having second thoughts about this direction. This "ripples in spacetime" thing seems dubious, despite my source. On page 563 Zee is actually referring to an description by a science writer rather than discussing "ripples" himself.

On page 566 Zee shows that any single particle does not move when a gravitational wave passes by. This is a consequence of Riemannian spacetime: it's local flat.

My take is that the "ripple in spacetime" analogy fails because "fabric" analogy fails. There is no extended medium, no aether to ripple.

What we can say, as Zee does, is the wave alters the relative positions of particles in an oscillatory pattern. This is what LIGO measures: the relative positions of two masses.

So now I would say:

• A gravitational wave alters the relative position of masses in an oscillatory fashion, propagates at the speed of light, and is produced by the relative motion of gravitating masses.

Johnjbarton (talk) 00:53, 10 March 2026 (UTC)

Thanks for the follow-up.

I agree that phrases like "ripples in spacetime" or "bending the fabric of spacetime" are informal and metaphorical. They’re widely used in science communication to help non-specialists visualise the idea, but they aren’t meant as literal descriptions of GR’s mathematics or physical content.

That’s why, a while back, I edited the article to encapsulate that line in quotation marks — to indicate to readers that it is a pedagogical metaphor rather than a technical description. If it still seems potentially misleading, we could certainly add some brief efn note(s) clarifying the precision of such language.

Regarding the alternative definition, I have a few concerns:

• It defines gravitational waves in terms of how they influence matter, rather than what they physically are. For example, sound waves can cause matter to vibrate, but that effect is not part of the definition of sound itself.
• The use of the adjective "oscillatory" reintroduces the earlier issue of suggesting periodicity (whether exact, approximate, or damped). While many astrophysical sources do produce approximately periodic waveforms, gravitational waves can also be aperiodic — for example, bursts, chirps, or other broadband signals from mergers or asymmetric collapse events.
• By analogy, defining gravitational waves this way would be similar to defining electromagnetic waves as "waves that oscillate charged particles, propagate at the speed of light in vacuum, and are produced by accelerating charges." That describes how EM waves affect matter and how they’re generated, but it doesn’t describe what an EM wave is (i.e. a propagating disturbance in the electromagnetic field). The same distinction applies here.

For these reasons, I think the current definition — which describes gravitational waves as propagating spacetime curvature disturbances — remains closer to the standard GR treatment found in sources like Carroll, Schutz, MTW, and LIGO’s technical explanations. It has been refined since its initial introduction, and although the flow is a bit different from the original wording I proposed, it still seems accurate and avoids the issues mentioned above.

Kind regards, Xyqorophibian (talk) 07:43, 10 March 2026 (UTC)

Thank you for the sources! Let me start with your list.

• "rather than what they physically are." I guess this will be the root of our disagreement. Waves are disturbances: their physical nature is defined by their influence on matter. They can only be detected by measuring a property of matter across time or space.
• oscillation. Can you point me to the part of Abbott that supports the idea of waves that are not oscillatory? Similarly Maggiore. Page 25 of Maggiore describes the effect of GW on test masses and on page 27 ... In this setting the definition of GWs is relatively clear: the background space-time is flat, and the small fluctuations around it have been called "gravitational waves". The term "waves" is justified by the fact that, in a suitable gauge, $h_{\mu \nu }$ indeed satisfies a wave equation. Similarly Carroll chapter 7 talks about test particle oscillation. I have a hard time coming up with any case where a gravitational wave would not be oscillatory simply because the bodies being strained are in a field to begin with.
• EM analogy. Both waves are the transmission of changes in force across distance due changes in positions of bodies. I would agree that both could be described as "a propagating disturbance in a field" and if we can find a good source for this form we should add it.

Based on this I draw two conclusions: We should have multiple definitions because there is no single correct way to describe GW and we do need to use the oscillations of space time curvature definition despite its many pitfalls. More below. Johnjbarton (talk) 16:34, 10 March 2026 (UTC)

Hi, let's go through this.

• It's correct that waves are (propagating) disturbances, but their nature is inferred and observed by their effects on matter — not defined by them. In here, the distinction between behaviour and definition is important. To exemplify again, sound waves may vibrate a tuning fork and radio waves can induce currents in an antenna, but those aspects of them aren't ontological.
• Carroll and Maggiore introduce gravitational waves using the standard monochromatic plane‑wave example because it is the simplest analytic solution for illustrating the TT gauge and geodesic deviation. That choice is pedagogical rather than restrictive: the linearised Einstein equations allow arbitrary time‑dependent perturbations.

In the LIGO/Virgo literature (e.g., Abbott et al.), gravitational‑wave signals are classified into continuous waves, chirps, bursts, and stochastic backgrounds. Only continuous waves are strictly periodic; chirps and bursts are explicitly non‑periodic. GW150914 itself is a chirp rather than a steady oscillation.

On the point about “bodies being strained in a field”: in GR the motion of freely falling masses follows the time‑dependence of the curvature perturbation via the geodesic deviation equation. A sinusoidal wave produces oscillatory motion, but a chirp produces a frequency sweep, a burst produces a single transient displacement, and the memory component produces a permanent offset.

So the detector response mirrors whatever waveform is present; it is not always oscillatory. The background gravitational field does not force periodic motion unless the wave itself is periodic.

• Those sources support my definition, in the sense that they treat gravitational waves as time‑dependent perturbations of the metric or curvature of spacetime, rather than as oscillations of a gravitational field.

I don't think multiple definitions is what the article reads, rather multiple descriptions that are all compatible with the definition currently in place is what should be aimed for.

Kind regards, Xyqorophibian (talk) 23:54, 10 March 2026 (UTC)

A gravitational wave alters the relative position of masses in an oscillatory fashion, propagates at the speed of light, and is produced by the relative motion of gravitating masses. -- Fwiw, as a layperson, I would find this summary of the origin/behavior/effect of gravitational waves to be useful descriptive information, even if it's in addition to, rather than instead of, the definition currently in place. -- Avocado (talk) 11:22, 10 March 2026 (UTC)

Well, I suppose there'd be nothing wrong with there being a mention of the way gravitational waves alter (in an oscillatory fashion, if the wave exhibits some sort of periodicity) the relative positions of masses' they encounter, and there's already line in the article that partially hints to what @Johnjbarton's definition specified:

As a gravitational wave passes an observer, that observer will find spacetime distorted by the effects of strain. Distances between objects increase and decrease rhythmically as the wave passes, at a frequency equal to that of the wave.

There is conceptual equivalence between the two, the main difference being that John's version is better from the stance of scientific accuracy and technical language. An improvement to make from here would be to change that line into something like this:

A passing gravitational wave produces a time‑dependent change in spacetime geometry that alters the relative separation of freely falling masses, reflecting a curvature disturbance rather than any mechanical deformation of a medium. The changing geometry causes the separation between freely falling masses to vary in a pattern that mirrors the waveform of the disturbance, taking an oscillatory form (with a frequency equal to that of the wave's) when the wave itself is periodic.

This keeps the intuitive description of what an observer would notice, but avoids suggesting that spacetime behaves like a material undergoing mechanical strain. It also avoids assuming strict periodicity, which matters because many astrophysical signals — such as bursts and chirps — do not have purely oscillatory waveforms.

If there are no objections, I’ll go ahead and implement this wording, as it seems to address the issues raised while preserving the intended meaning. Kudos to the two of you for the constructive discussion :)

Kind regards, Xyqorophibian (talk) 12:34, 10 March 2026 (UTC)

time‑dependent change in spacetime geometry? Either a change in spacetime geometry or a time‑dependent change in geometry (probably the latter, as change may imply the existence of time outside of spacetime). catslash (talk) 14:35, 10 March 2026 (UTC)

yes these are some of the problems with talking about spacetime waves. Spacetime is local and frame dependent. I object to "change in spacetime geometry." Geometry, the measurement of space, does not change. The strain field is changing. Changes in spacetime curvature makes sense. Thus test particles, which move as if in a curved spacetime, now move as if in a spacetime with a different curvature. Johnjbarton (talk) 16:55, 10 March 2026 (UTC)

Ok I take part of this back. Schutz cite below has a good discussion in his chapter on "Measuring the stretching of space". Free bodies respond to GW by moving relative to each other, but a ruler fixed to one of the bodies does not change in length because it is subject to EM forces maintaining that length. This is the same idea as expansion of the universe. The space between bodies subject to a GW changes. So "geometry, the measurement of space" does change, but its not "change in spacetime geometry". Johnjbarton (talk) 18:06, 10 March 2026 (UTC)

Now replying to Xyqorophibian proposal:

A passing gravitational wave alters the relative separation of freely falling masses, reflecting a disturbance in local spacetime curvature. The separation varies in a pattern that mirrors the waveform of the disturbance.

I basically deleted bits that I think are redundant, unsourced, or more complex than we should start with. But now its probably not what you had in mind :-(.

We should try to include some of these sources in the article. Johnjbarton (talk) 18:17, 10 March 2026 (UTC)

Hi.

Thanks @Catslash for raising this terminology concern and @Johnjbarton for polishing the statement up.

I think the revision is a nice, concise trim. The extra parts in the version I proposed were mainly there to help with intuition (e.g. drawing parallels with mechanical deformation but clarifying it is distinct) and to exemplify oscillatory behaviour (e.g. same frequency) when the waveform exhibits periodicity, not that they were really relevant.

Only final touch I’d add is linking the relevant terms:

A passing gravitational wave alters the relative separation of freely falling masses, reflecting a disturbance in local spacetime curvature. The separation varies in a pattern that mirrors the waveform of the disturbance.

Kind regards, Xyqorophibian (talk) 00:03, 11 March 2026 (UTC)

More sources:

• Thorne, K. S. (1994). Black holes and time warps : Einstein's outrageous legacy. United Kingdom: WW Norton. pg 48 ripples of tidal force (ripples of "spacetime curvature") called gravitational waves. pg 358 Since spacetime curvature is the same thing as gravity, these ripples of curvature are actually waves of gravity, or gravitational waves. Pg 362 The gravitational wave's tidal forces (curvature ripples) are analogous to light waves or radio waves: they travel from their source to the Earth at the speed of light, oscillating as they travel. Notes three difference from Moon's tidal waves.
• Susskind, L. (2008). The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics. United States: Little, Brown. pg 326 spreads out...in the form a a ripple of curvature or a gravitational wave. Gravitational waves are to mass what electromagnetic waves are to electric charge.
• Hawking, S. (1996). The Illustrated A Brief History of Time: Updated and Expanded Edition. United Kingdom: Random House Publishing Group. pg 117 General relativity predicts the heavy objects that are moving will cause the emission of gravitational waves, ripples in the curvature of space that travel at the speed of light. These are similar to light waves, which are ripples of the electromagnetic field, but they are much harder to detect.

So for this crowd at least, the "oscillation" aspect can be capture by "ripples of curvature". Johnjbarton (talk) 22:00, 10 March 2026 (UTC)

Hi, thanks for gathering these additional sources. They’re helpful for the “ripples in spacetime” line in the introduction — Thorne, Susskind, and Hawking all use that metaphor, and it’s good to have citations for it.

I’ll incorporate those for the descriptive wording, and use the technical sources already mentioned earlier (Carroll, Maggiore, Schutz, MTW, LIGO/Virgo) for the definition itself. I’ll also go ahead and update the line we discussed accordingly.

Thanks again for pulling these together.

Kind regards, Xyqorophibian (talk) 12:00, 11 March 2026 (UTC)

Your version

• Gravitational waves are waves of spacetime distortion and curvature produced by the relative motion of gravitating masses and which propagate away at the speed of light.

I remove distortion:

• Gravitational waves are waves in spacetime curvature produced by the relative motion of gravitating masses and which propagate away at the speed of light.

but I also altered the linking.

The sources should not be jamming in the intro unless the content is controversial. I personally don't take our discussion above as controversy so much as reaching a mutual understanding based on sources. So I think the sources should be in the body of the article per WP:LEAD#Citations. Johnjbarton (talk) 17:05, 11 March 2026 (UTC)

Thanks — I’m fine with removing “distortion”; “waves of spacetime curvature” is the standard phrasing used in the sources, and it keeps the definition aligned with the GR literature. However, “of”, not “in”, is the grammatically correct and source‑supported phrasing, so that part should be corrected. I’d also relink “spacetime curvature” to curved spacetime to be more direct.

I'd polish up the definition to be this:

---

Gravitational waves are waves of spacetime curvature that propagate at the speed of light and are produced by the relative motion of gravitating masses.

---

On the citations: the four GR textbooks are grouped together because they all emphasise the disturbance/curvature picture of gravitational waves, and I wanted to reflect that this interpretation is consistently supported across the literature. Flanagan & Hughes also supports that picture, but it additionally provides an explicit statement about propagation at the speed of light, so it is placed at the end of the sentence where that specific claim is made. Since WP:LEAD recommends avoiding technical citations in the lead when the material is developed in the body, I’m happy to relocate these sources to the Introduction section.

In the Introduction section, the material mentioned in the definition is further elaborated upon and develops the GR picture of curvature, moving masses, and wave propagation. In particular, the first paragraph

In Albert Einstein's general theory of relativity, gravity is treated as a phenomenon resulting from the curvature of spacetime. This curvature is caused by the presence of mass. (See: Stress–energy tensor) If the masses move, the curvature of spacetime changes. If the motion is not spherically symmetric, the motion can cause gravitational waves which propagate away at the speed of light.

is a natural place to relocate the sources, and for some reconstruction. I'd redo it into this:

---

In Albert Einstein's general theory of relativity, gravity is treated as a phenomenon resulting from the curvature of spacetime, which is caused by the presence of mass. (See: Stress–energy tensor) If the masses move, the curvature of spacetime changes; and if the motion is not spherically symmetric, it can emit propagating curvature disturbances—i.e., gravitational waves—which radiate outward at the speed of light.

---

In the above revision of the introduction's first paragraph, several of the currently unsubstantiated details have become sourced, the currently-present but unrelated source (i.e. Penrose) is omitted and the transition from GR (the context) into GWs (the phenomenon) is smoother, clearer and more direct.

I believe this would be the optimal approach to take.

Kind regards, Xyqorophibian (talk) 01:10, 12 March 2026 (UTC)

Sounds great. You should just go ahead. Please be careful to explain any removed sources. Johnjbarton (talk) 03:23, 12 March 2026 (UTC)

Implemented! — thanks. Xyqorophibian (talk) 03:51, 12 March 2026 (UTC)

Ok so feedback: the pattern of citations in that paragraph raises red flags for me and I guess other editors. Many citations in the middle of sentences is a signal of potential WP:synthesis: attempting to create a new fact by pasting together multiple sources which verify unconnected facts. I know that is not going in here, but rather an effort be very concise and accurate. Four sources on two words is a sign that the citations are there for some other purpose than verifying the content. In this case I guess you think these are all worthy sources. More than one source or two if one is pop-sci makes verification harder. Johnjbarton (talk) 15:28, 12 March 2026 (UTC)

Each citation in that paragraph supports a distinct claim (Hartle for curvature; Wald for curvature caused by mass; Poisson & Will for dynamical curvature and emission; and Carroll/Maggiore/Schutz/MTW for identifying those disturbances as gravitational waves). There’s no synthesis, but I agree the inline pattern can look dense at a glance.

The density mainly comes from having several mid‑sentence citations. I considered alternatives like moving citations to the end of sentences and using descriptive named references, but that still wouldn’t meet WP:V’s requirement to cite at the point of verification, and it would make it harder to see which source supports which specific claim.

If it helps with the optics, I can trim the GW‑identification sources down to the two most relevant ones while keeping the rest of the sourcing structure intact. Would that address the concern you raised? Xyqorophibian (talk) 09:12, 13 March 2026 (UTC)

References

Displacement inversely proportional to distance rather than distance squared

The article https://en.wikipedia.org/wiki/Gravitational_wave states: "A passing gravitational wave alters the relative separation of freely falling masses, reflecting a disturbance in local spacetime curvature. The separation varies in a pattern that mirrors the waveform of the disturbance. The magnitude of this effect is inversely proportional to the distance (not distance squared) from the source."

The claim is supported by a reference, and I was just watching a YouTube video (https://www.youtube.com/watch?v=k1vaFNu4ZYE) in which Physicist Tessa Baker at the University of Portsmouth, UK said exactly the same thing, so despite this being somewhat unexpected to me, I'll take it as an established fact.

However once you accept that fact, if you also accept that gravitational waves carry energy, it follows that for energy to be conserved in a spherical expanding shockfront (ignoring negligible frictional loses as the gravitational wave shockfront passes through space), the energy passing through a square metre of the surface of a sphere centred at the origin of the gravitational wave must be inversely proportional to the distance from the origin squared, otherwise it would tend towards infinite energy as it expanded, and it follows from that, and the fact that the displacement caused by the passing of the gravitational wave is proportional to the distance from the origin, that the energy associated with a given displacement is proportional to the square of the displacement - kind of like a spring. I expect gravitational wave physicists already know that.

I ran that idea by ChatGPT, and it referred me to a couple of articles which it basically said kind of supported my perspective, but to be honest, I had trouble following them:

1. Simplified derivation of the gravitational wave stress tensor

According to ChatGPT this paper explicitly shows that the effective stress–energy of gravitational waves arises from terms quadratic in the perturbation hμν​:

the stress-energy comes from terms “quadratic in hμν​”

That is exactly your point:

• amplitude h ∝ displacement/strain
• energy ∝ h^2

This is the rigorous GR version of your “spring-like” intuition.

---

2. Effective Gravitational Wave Stress-energy Tensor (arXiv)

According to ChatGPT this paper explains that:

gravitational radiation is described by an effective stress-energy tensor governing energy transport

Combined with standard results (shown explicitly in many GR texts and reviews), this tensor has the schematic form:

TμνGW​∼⟨∂h∂h⟩ So:

• energy density ∝ (∂h)^2
• ⇒ energy ∝ h^2

Again, this is your conclusion in formal language.

---

____________

So anyway, I think the article could be improved by incorporating some of this information, perhaps right after the section in the article that states: "A passing gravitational wave alters the relative separation of freely falling masses... The magnitude of this effect is inversely proportional to the distance (not distance squared) from the source." add something like: "The energy carried by gravitational waves is proportional to the square of the wave amplitude (metric perturbation), so although the amplitude falls off as 1/r, the energy flux falls off as 1/r^2, ensuring conservation of energy." MathewMunro (talk) 22:13, 17 April 2026 (UTC)

Your mistake was asking GPT. I'll do you the favour of not directly hatting your comment, but be aware that WP:LLMTALK is a thing. In return, please do us the favour of not relying on GPT as a reliable source, because most of what you copied in was wrong in some subtle and other not so subtle ways, and about the only fully correct statement that was made is that T\mu\nu is second order in h\mu\nu, which is the tensorial version of the high school E = 1/2 kx^2. Fermiboson (talk) 22:27, 17 April 2026 (UTC)