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we have p18 an integral on space time M. The author takes a 3 dimensional space like Cauchy surface ##\Sigma## which separates M in two regions, the future and the past of ##\Sigma##. He gets so the sum of two integrals on these regions. He writes then let us integrate each of them by parts. The fact that ##\Sigma## is a boundary for these regions is obvious. the vector n orthogonal to the boundary occurs in the result but i think that this uses the (- +++) metric. What is the formula used to integrate by parts in relativity?

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# Integration by parts in spacetime

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