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

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The discussion centers on a potential typo in Schutz's book regarding the four-acceleration in General Relativity. Participants clarify that the text is accurate, stating that in the momentarily comoving inertial frame, the time component of the four-acceleration is indeed zero. It is emphasized that the only non-zero component of the four-velocity is the zeroth one, leading to the correct interpretation of the four-acceleration's orthogonality to the four-velocity. However, there is a consensus that the writing lacks clarity, suggesting it would be better if Schutz had specified that the four-velocity has only a non-zero zeroth component. Overall, while the physics is sound, the need for clearer writing and better editing is noted.
Ahmed1029
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I'm wondering is I'm missing something, or this should be " a non-zero component"?
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The book is correct. In the momentarily comoving inertial frame the time component of the four-acceleration is indeed 0.
 
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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".
 
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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.
 
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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.
 
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