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Comments on How are gravitational waves derived?

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How are gravitational waves derived?

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Gravitational waves can be derived from the non-linear Einstein field equations and since they are by definition waves they must obey the wave equation:

$u_{tt}=c^{2}u_{xx}$ but in General Relativity time and space are not fixed so how are $t$ and $x$ defined for a gravitational wave?

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Linearization (1 comment)
Linearization
peterh‭ wrote about 12 hours ago

While the GR is non-linear, it can be considered linear for small spacetime distortions. That is the linearized general relativity. As being linear, wave propagation and similars are happily coming out.