I know Maxwell equation shows that it is the electric and magnetic properties of empty space which is why speed of light is constant, but what about gravitational waves? I have visited many answers but so far none seems satisfactory to me. Can we prove that gravitational wave is also a constant?
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1It's part of the general relativity theory. This Wikipedia article might be helpful: https://en.wikipedia.org/wiki/Speed_of_gravity (including linked articles or references, if you want more) – riddleculous Jan 21 '20 at 09:51
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2You'll find this in any GR book. We use an ansatz $h^{ab} = A^{ab}\exp(ik_ax^a)$ and substituting this into the linearised equation we find $\mathbf k$ is a null one-form i.e. the wave travels at $c$. – John Rennie Jan 21 '20 at 10:07
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@JohnRennie: I can't find the equation but is it the rate of energy loss due to inspiral of compact stars. – user6760 Jan 21 '20 at 10:43
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Possible duplicates: https://physics.stackexchange.com/q/254628/2451 , https://physics.stackexchange.com/q/255361/2451 and links therein. – Qmechanic Jan 21 '20 at 11:18
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@user6760 the equation for the power emitted as gravitational waves is given in my answer to Is it possible to produce gravitational waves artificially?. – John Rennie Jan 21 '20 at 11:20
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This is because gravitational waves are massless. Special relativity states that massless matter moves at $c$ in vacuum.
my2cts
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How do you manage to post an answer after this question was closed! What socery is this? ;D – user6760 Jan 21 '20 at 12:27
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