Is the Speed of Light Truly Constant in General Relativity?

[Naty1]

These issues are fairly complex and explaining them accurately and unambiguously to someone who is asking a "simple" question is not so simple. Dr Greg's posts above are, I believe, precisely accurate. Rereading my own initial post, I would now change a few words, but likely the poster would not have gained any additional insights anyway...

The speed of light being constant to all observers is one of the fundamental aspects of special relativity, so it can't be different in general relativity, as it arose from special relativity.

This statement is not precisely accurate because special relativity implies constant velocity and no curvature of space (no gravity); general relativity involves curvature of space and acceleration and only simplifies to special relativity under certain circumstances...no gravity, no acceleration...