<p>In empty space, at large distances from masses and at small amplitudes, GWs propagate at the speed of light. This does <strong>not</strong> apply near the source, because there is a large mass and the amplitude of the GW is very large. How large is <span class="math-container">$v_{GW}$</span> at a distance of 1 AU from Algol? There, two suns orbit each other within 2.87 days.</p>

CC BY-SA 4.0
2023-11-14T18:58:45.843Z
Why should the speed be different to $c$?
ProfRob
CC BY-SA 4.0
2023-11-14T22:48:04.063Z
The Einstein field equations

$G_{µν} ≡ R_{µν} -\frac{1}{1}g_{µν}R = 8πT_{µν}$

express the equivalence between matter-energy and curvature. At large distances from masses $T_{µν}$ can be neglected and (at small amplitudes!) linearized. These simplifications are inadmissible in the vicinity of stars.
9herbert9
CC BY-SA 4.0
2023-11-15T06:50:27.450Z
1 AU from Algol is still very far from algol. All the weak field approximations are still valid. Actually, since Algol is made of stars, not black holes, I would say that you can always linearize the field, no matter the distance
Prallax
CC BY-SA 4.0
2023-11-15T14:32:40.047Z
That's hard to believe. Algol produces about $P=10^{10}$ watts of GW-power ([Gravitational Waves in Astrophysics]https://webspace.science.uu.nl/~proko101/JeroenBurgers_gw3.pdf), which is not a "small" amplitude. Where can I find a calculation?
9herbert9
CC BY-SA 4.0
2023-11-15T16:04:39.727Z
$P = 10^{10}$ Watts is a power; it is not even a flux, let alone a strain amplitude. You write, **with certitude**, that you think the wave speed (or the speed of whatever the disturbance in the metric is called) is propagating at some different speed to $c$, with no indication of why that should be, or any reference to a reputable source that claims it is. This seems to be another question where you have decided what the answer is already.
ProfRob
CC BY-SA 4.0
2023-11-15T17:04:28.573Z
@9herbert9 - 10 ^ 10 watts represents a truly tiny amplitude; the power is comparable to a single electric generating station on earth, and an infinitesimal fraction of the electromagnetic radiation produced by the system.  The GW power from colliding black holes peaks on the order of 10^50 watts, 40 orders of magnitude higher.  The GW amplitude from the Algol components orbit that would be observable 1 AU from the primary would be millions of times smaller than LIGO observes from colliding black holes at cosmological distances.
antlersoft
CC BY-SA 4.0
2023-11-15T21:51:02.997Z
Comparing powers does not provide a solution. It would be better to know at what value $h_{critical}$ it becomes pointless to work with the linearized form of Einstein's field equations. Who knows a solution?
9herbert9
CC BY-SA 4.0
2023-11-15T21:56:02.637Z
$h_{\rm critical} \ll 1$
ProfRob
CC BY-SA 4.0
2023-11-17T19:15:35.970Z
If gravity waves do not travel at c, then gravitons, being massless, can not exist.  That would mean quantized gravity and string theory are nonstarters.
eshaya
<general-relativity><gravitational-waves>
$v_{GW}$ near a binary star?
9herbert9
# $v_{GW}$ near a binary star?

(Asked by: username_0 on 2023-11-14)

In empty space, at large distances from masses and at small amplitudes, GWs propagate at the speed of light. This does **not** apply near the source, because there is a large mass and the amplitude of the GW is very large. How large is $v\_{GW}$ at a distance of 1 AU from Algol? There, two suns orbit each other within 2.87 days.

**Tags:** general-relativity, gravitational-waves
> **Comments:**
> **username_1**: Why should the speed be different to $c$?  
> **username_0**: The Einstein field equations  $G_{µν} ≡ R_{µν} -\frac{1}{1}g_{µν}R = 8πT_{µν}$  express the equivalence between matter-energy and curvature. At large distances from masses $T_{µν}$ can be neglected and (at small amplitudes!) linearized. These simplifications are inadmissible in the vicinity of stars.  
> **username_2**: 1 AU from Algol is still very far from algol. All the weak field approximations are still valid. Actually, since Algol is made of stars, not black holes, I would say that you can always linearize the field, no matter the distance  
> **username_0**: That's hard to believe. Algol produces about $P=10^{10}$ watts of GW-power ([Gravitational Waves in Astrophysics]https://webspace.science.uu.nl/~proko101/JeroenBurgers_gw3.pdf), which is not a "small" amplitude. Where can I find a calculation?  
> **username_1**: $P = 10^{10}$ Watts is a power; it is not even a flux, let alone a strain amplitude. You write, **with certitude**, that you think the wave speed (or the speed of whatever the disturbance in the metric is called) is propagating at some different speed to $c$, with no indication of why that should be, or any reference to a reputable source that claims it is. This seems to be another question where you have decided what the answer is already.  
> **username_3**: @9herbert9 - 10 ^ 10 watts represents a truly tiny amplitude; the power is comparable to a single electric generating station on earth, and an infinitesimal fraction of the electromagnetic radiation produced by the system.  The GW power from colliding black holes peaks on the order of 10^50 watts, 40 orders of magnitude higher.  The GW amplitude from the Algol components orbit that would be observable 1 AU from the primary would be millions of times smaller than LIGO observes from colliding black holes at cosmological distances.  
> **username_0**: Comparing powers does not provide a solution. It would be better to know at what value $h_{critical}$ it becomes pointless to work with the linearized form of Einstein's field equations. Who knows a solution?  
> **username_1**: $h_{\rm critical} \ll 1$  
> **username_4**: If gravity waves do not travel at c, then gravitons, being massless, can not exist.  That would mean quantized gravity and string theory are nonstarters.  

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