In both Newtonian gravity and special relativity, every frame of reference can be described by a coordinate system covering all of time and space. How does this work in general relativity? When an observer watches matter falling into a black hole, or observes a distant galaxy receding from ours, can we describe what they see in terms of a certain coordinate system that is tied to that observer?
Related:
The following are very similar questions but at a fancy mathematical level, and focusing on the technical details such as charts and manifolds:
How a reference frame relates to observers and charts?
What does a frame of reference mean in terms of manifolds?
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