Clarification on mass-energy tensor and 4-velocity.

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SUMMARY

The discussion centers around the equation \(\frac{dU^b}{d\tau}=U^a \nabla_a U^b\) from Woodhouse's book on General Relativity (GR), specifically on page 34. The user seeks clarification on the validity of this equation, which describes the change in 4-velocity \(U^b\) along a worldline. The response indicates that by selecting a specific frame where \(U^a=(1,0,0,0)\), the equation's correctness becomes evident, demonstrating the application of covariant differentiation in GR.

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I have next question, we have in the next printcreen the equation:
[tex]\frac{dU^b}{d\tau}=U^a \nabla_a U^b[/tex]
why is this right?
(the printscreen is from the book of Woodhouse in GR, page 34)

Thanks.
 

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Ok, I think I can see why this is right, we pick a frame where [tex]U^a=(1,0,0,0)[/tex].

Clumsy me.
:-)
 

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