gr S. Carroll caltech http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll3.html

http://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll3.html

Lecture Notes on General Relativity - S. Carroll - NED

ned.ipac.caltech.edu/.../Carroll3.html

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California Institute of Technology

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The primary usefulness of geodesics in general relativity is that they are the paths .... We have already argued, using the two-sphere as an example, that parallel ...

Lecture Notes on General Relativity - S. Carroll - NED

ned.ipac.caltech.edu/.../Carroll7.html

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California Institute of Technology

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(In this section the word "sphere" means S², not spheres of higher dimension.) ..... The geodesic equation therefore turns into the following four equations, where .... In general relativity the situation is different, but only for r sufficiently small.