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Can it really be said that something as large as a galaxy can have a "shape", which the positions of its constituent stars are their positions at various times in the past? A star 100K ly from us is no longer in the position we see it, same for stars 50K ly away and so on. Thus, a "shape" is not sufficiently deterministic and is only phenomena from a particular perspective; the shape doesn't exist.

Thus, the wave density models, which assume a universal "now", would be inaccurate. I know these time differentials must be considered, I can't image they're ignored, but it's never mentioned if it's just insignificant or built into the model. I'm sure this is a naive question, but I never come across anything that addresses it.

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The same question has been asked in somewhat different guises before (e.g. How does space time differ within a galaxy? ; What is the relative time difference between us and a star system in outer layer of our galaxy? ), but the answer is similar:

A typical orbital period for something at a "galactocentric radius" of say 25,000 light years (similar to the Sun's distance from the galactic centre) is about 200 million years.

i.e., the light travel time is 10,000 times faster than the typical timescales for things to move significantly within the galaxy. In other words, the components of the galaxy are not moving relativistically - typically at $v/c \sim 10^{-4}$. Therefore the concept of a galaxy-wide time coordinate is reasonable and it is therefore quite safe to ignore the effect you are talking about at the levels of precision required for most purposes.

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