Does anyone have a textbook reference for the rigorous definition of a family of observers? Wald uses the term a lot but never actually defines it i.e. is it a congruence of unit time - like world lines defined on a proper open subset of the space - time or is it a congruence defined over the entire space - time or does it even have to be a congruence at all (i.e. can two worldlines in the family intersect)? To this entire family we give an orthonormal frame field that is supposed to characterize how the measuring apparatuses of each observer is oriented but what is the rigorous link between the mathematical and physical definition here (i.e. what constitutes the measuring apparatuses - are they just a physical way of characterizing the orientation of the orthonormal frame field?). I believe MTW actually gives proper definitions of these things but the book is huge I got lost trying to find anything pertinent so I'm hoping someone else possibly knows the relevant sections or has other texts to look at. Thanks!