The term "Relative Velocity" has a somewhat vague definition in General Relativity - perhaps it doesnt really have a definition at all! What is the relative velocity of two observers with respect to one another when the spacetime that they are moving in is curved? In SR one compares the velocity vector of one observer with the 4-velocity vector of the other by parallel transporting it. In flat space there is exactly one way to do this - parallel transport the 4-velocity vector along the straight line between the two. As a result there is a definitive notion of relative velocity between two observers in SR. In GR, the spacetime is necessarily curved and hence there is perhaps a great number of ways to parallel transport the 4-velocity vector, hence a great number of ways to define what one means by relative velocity. I have not read anywhere an attempt to give a proper definition to relative velocity in GR. I am certainly not saying that this is possible or that relative velocity should even be given a definition in GR - it may be rediculous! Never-the-less I will attempt the task in this thread, hopefully with the help of others. My main source of information is the book "General Relativity" by Robert Wald which Pervect suggested I read, from the thread in this forum titled "Relative Velocity". This thread becomes the second part in my quest to define relative velocity in GR. Wald does spend a bit of time discussing redshift, which I like - particularly chapter 6.3. However, he does not explicitly discuss relative velocity - but I feel that from what he has written I can make the following proposal: relative velocity between two observers (In GR) is a physical quantity derived from the frequency shift of a light ray connecting the two observers. That is, I want to define relative velocity in GR as being directly related to the redshift. I understand that this will not be quite universal, that is, I dont think I will be able to define a frequency shift explicitly in every GR setting - BUT - in the cases where I am able to define a frequency shift I WILL be able to define relative velocity. This is the definition I want to give to the term "Relative Velocity" of two observers in GR. Any thoughts?