I Max Amplitude Gravitational Waves: 2?

[James Essig]

I am curious as to what the maximum amplitude of gravitational waves is. I have read that the maximum amplitude as such is equal to two but I cannot seem to find again a reference that states this clearly.

 

[PeterDonis]

I have read that the maximum amplitude as such is equal to two

Where have you read that?

 

[James Essig]

I am not sure. My memory seems to indicate that I read of the value of two in a Wikipedia article but upon searching related Wikipedia topics, I cannot find any verifying statements. Wikipedia is far from the most credible sources, so perhaps a more credible source is preferred. By a factor of two, I mean the extent of the space of maximum space contraction is 50 % of the extent of the space of maximum space expansion as a result of a passing gravitational wave.

 

[Dale]

I have never heard this before. I suspect that your recollection is mistaken.

 

[PeterDonis]

By a factor of two, I mean the extent of the space of maximum space contraction is 50 % of the extent of the space of maximum space expansion as a result of a passing gravitational wave.

I have never heard this either so I agree with @Dale that your recollection is most likely mistaken.

As far as a general answer to your question, gravitational waves are standardly treated using the linearized approximation of GR, which assumes that any perturbations of the metric are small; since the size of the perturbation of the metric is the amplitude of the gravitational wave, that would mean that the amplitude of gravitational waves should be small. Of course "small" does not have a precise definition; it depends on the problem and on how accurate you want your predictions to be. But generally speaking, if the perturbation is not small, the linearized approximation is no longer valid, which means whatever you're studying is no longer usefully viewed as a "gravitational wave"; it's a more general curved spacetime.