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In The Large Scale Structure of Space-Time, Hawking and Ellis refer twice (page 4, page 78) to non-rotating families of geodesics.

I don't know what that means. Is a rotating geodesic one that represents an object revolving around another object? Is it as simple as that?

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What do Hawking/Ellis mean exactly by "non-rotating families of geodesics"?

They mean geodesic congruences with vanishing vorticity tensor. The definition of vorticity tensor could be found in Hawking&Ellis on page 82, or in wikipedia.

Is a rotating geodesic one that represents an object revolving around another object?

It is not a geodesic that rotates but a family of geodesics, and vorticity tensor represents the rate of rotation for neighboring curves.

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  • $\begingroup$ And page 69 of Hawking/Ellis has a definition of congruences.... Page 216 of Wald's book General Relativity has a good description of congruences as well. $\endgroup$
    – John
    Commented Dec 13, 2022 at 23:30

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