Does the principle of invariant light speed still hold in a non Inertial frame of reference?
I thought that it held locally since any region of spacetime is locally flat.
So the claim that the speed of light is invariant "locally" in SR doesn't really mean anything, unless you explain what you mean of course.
Yes, locally could mean this. If any "photon" is (sufficiently close to being) coincident with any observer, accelerated or non-accleerated, in both special and general relativity, then, by using (sufficiently small) standard clocks and rulers, the observer measures the speed of the photon to be c. If the photon and the observer are not coincident, then, as Vanadium 50 has pointed out, the concept of speed speed is subtle (even more so in relativity), and, as pointed out by atyy and Fredrik, coordinate speed can take on any value.If we use the "proper reference frame" of an accelerating observer (i.e. the coordinate system constructed using the standard synchronization procedure), the coordinate speed of light emitted by the observer will depend on a lot of different things, but if he emits the light at the origin of his coordinates, it will at least start out with speed c. I guess that's one thing we could mean by "holds locally" (but I'd rather not use phrases like that).
I don't see why "non-inertial frame of reference" implies flat spacetime. Am I not right now in a non-inertial frame of reference (I'm not freefalling as I type) in a spacetime that is curved?The question is about Minkowski spacetime, which is globally flat.
Yes. I gave my answer for the "global" speed of light in special relativity, which is restricted to flat spacetime.I thought that it held locally since any region of spacetime is locally flat.
Strictly speaking "locally" in the above means "at a point" (George Jones's "tangent space"). It is not strictly true for any finite piece of spacetime (unless spacetime is flat, and an inertial frame is used), but practically speaking, a finite piece of spacetime that is small enough will be close enough to a "point" given limited sensitivity of experimental equipment.By "locally" I just meant "nearby" - in the sense that the surface of a sphere is flat if one looks at a small enough piece of it. Maybe I used the term inappropriately.