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World function

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The value of the integral

taken along a geodesic joining two points and in (geodesically-convex) space-time. Here is given by a parametrization , where is a canonical parameter and . The world function is equal, up to sign, to half the square measure of the geodesic joining and , and is a two-point invariant in the sense that its value does not change under coordinate transformations in a neighbourhood of and .

In flat space-time there is a system of coordinates such that

where

References

[1] J.L. Synge, "Relativity: the general theory" , North-Holland & Interscience (1960) pp. Chapt. II
How to Cite This Entry:
World function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=World_function&oldid=43496
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article