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For example, in the sentence "there is no incoming radiation at past null infinity".

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up vote 3 down vote accepted

Consider Minkwski space. "Past" means $t\to-\infty$, "infinity" means $r\to+\infty$, meaning infinitely far from your origin. "Lightlike" means you are going in that direction in the same way a photon would do, i.e. with $r/t=1$. In other words, imagine a photon that crosses the origin at a certain time. If you follow its geodesic in the past direction, you'll reach past null infinity.

No incoming radiation at past null infinity is a sound border condition: I think it means, in very rough terms, no energy can come from outside the universe.

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Thanks, you explained it well, and without the need to invoke Penrose diagrams, which are something I know nothing about. –  user12345 Jan 14 '13 at 21:59
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It corresponds to the $\scr{I}^-$ line of a Penrose diagram. "Null" means lightlike, "past lightlike" corresponds to the lower right boundary of Minkowski space, while "future lightlike" would be the upper right one.

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