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I have a question concerning the asymptotic boundary conditions on matter fields and the Riemann tensor. What is the precise relation between saying that "the matter fields go to zero at spatial infinity" and "the matter fields have compact support"? And how natural is it to state that the Riemann tensor has "compact support" on a certain spacetime? I would say that if the matter fields have compact support, the Riemann tensor also has, right?

Thanks!

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# Compact support of matter fields

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