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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Thread 'Physical Interpretation of Frame Field'

Moderator's note: Spin-off from another thread due to topic change. In the second link referenced, there is a claim about a physical interpretation of frame field. Consider a family of observers whose worldlines fill a region of spacetime. Each of them carries a clock and a set of mutually orthogonal rulers. Each observer points in the (timelike) direction defined by its worldline's tangent at any given event along it. What about the rulers each of them carries ? My interpretation: each...
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