I know that in Minkowsky space, the 4-velocity is normalize according to the following relation:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\eta_{\mu\nu} U^{\mu} U^{\nu} = -1[/tex]

Can someone explain to me ho this can be generalized to a normalization in a curved space with the following relation :

[tex]g_{\mu\nu} U^{\mu} U^{\nu} = -1[/tex]

The reference that I am using just use the previous expression without any justification and this bothers me.

Thanks!

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# Normalization of 4-velocity in general relativity

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