I Is this just a typo in Schutz' book on General Relativity?

[Ahmed1029]

I'm wondering is I'm missing something, or this should be " a non-zero component"?

 

[Dale]

The book is correct. In the momentarily comoving inertial frame the time component of the four-acceleration is indeed 0.

 

[Ibix]

No, it means that in the MCRF the only non-zero component of $\tilde{U}$ is the zeroth one (because the three velocity is zero by definition in that frame). Hence the four acceleration (which he's just proved is orthogonal to $\tilde{U}$) must take the form given.

I agree it's not particularly clearly written - it would be better if he'd said "$\tilde{U}$ has only a ${\tilde{U}}^0$ component".

 

[Ahmed1029]

Ah yes, it's clear now. I thought he meant that it had only one component taking the value zero, which didn't make sense.

 

[Ibix]

I must say this isn't the only thing I've found confusing in Schutz. The physics is sound enough, but I do feel like he really needed a better editor.