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There's only one kind of redshift in general relativity. The cosmological redshift, gravitational redshift, and special-relativistic redshift formulas are special cases of it, which apply to spacetimes with certain symmetries. If you put approximate Minkowski coordinates on a patch of spacetime that's small enough to be approximately flat, you'll find that ...


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Observed brightness (or magnitude) depends on the distance between the source and the observer. The further the distance, the fainter we will observe given the same source. If the distance r1 is measured between the source and the observer given the accelerating universe, then the distance r2 measured given the decelerating universe would be r2 < r1. ...


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