- #26

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I'm ashamed to say that I've never seen the derivation of the expression in SR either. Would you be able to show me, and/or suggest a book to read up on it?!It is a straight-forward generalisation of the corresponding SR expression. It is going to locally correspond to the same thing - the product of the wave vector with the observer 4-velocity.

Is it essentially then, that ##\delta v^{\mu}\propto R^{\mu}_{\;\nu}v^{\nu}## (where ##\delta v^{\mu}## denotes the change in the components of a vector under parallel transport around an infinitesimal loop and ##R^{\mu}_{\;\nu}## is the Ricci curvature tensor) and for a flat space ##R^{\mu}_{\;\nu}=0##, hence ##\delta v^{\mu}=0## and the components of a vector are invariant under parallel transport?!Construct the parallel transport around a loop as the contributions from several infinitesimal loops. This can be done since Minkowski space is simply connected. The change in the parallel transported vector around an infinitesimal loop is proportional to the curvature tensor, which for a flat space is zero everywhere.