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I have recently completed two courses in general relativity and am well versed in things like the ray chaudhuri equation, tetrads, etc. I had to give a 2hr talk on gravitational radiation to my class and so understand GWs at some relatively respectable level. What I am inquiring about is the formulation of the perturbation metric in a precise sense. What literature normally says is, $$g_{ab} = \eta_{ab} + h_{ab},$$ where $$h_{ab}\ll \eta_{ab}$$ for non-zero elements. What I want to know is whether there is a more precise definition of "small". More to the point is there a more fundamental point of view for using perturbation theory and when it is valid in differential geometry or math in general. Feel free to use big words ;)

J. Albert

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# Precise formuation of perturbations in GR

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