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Definition clarification needed, please: I am hoping to get physical sense of an "inertial frame".

Do inertial reference frames all have zero curvature for their spacetime?

So is an inertial frame just a flat metric?

(Sorry that the question is not too profound. I have read the Wiki article for inertial frame of reference, but I'm just not entirely sure.)

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Inertial reference frames must be locally flat; they must span a sufficiently small region of spacetime such that the spacetime is flat within their vicinity. This is always possible for spacetimes described by Riemannian manifolds.

If spacetime wasn't locally flat in a reference frame, it could be distinguished from an inertial reference frame by tidal forces. e.g. the curvature differing between your head and your toes.

Inertial reference frames must not be accelerating; they must be in free-fall in a gravitational field. An inertial frame, then, is not simply a flat metric. It is free-falling frame in a sufficiently small region of spacetime such that the curvature is flat.

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Thanks, innisfree :) – Bess Apr 28 '13 at 11:56
"If spacetime wasn't locally flat in a reference frame..." This doesn't make sense. Flatness doesn't depend on the frame of reference. Flatness means the Riemann tensor vanishes. Changing frames of reference can be accomplished by a change of coordinates. If a tensor is zero in one set of coordinates, it's zero in every other set of coordinates. – Ben Crowell May 28 '13 at 1:18
I mean that on scales greater than the characteristic curvature, we have geodesic deviation. So our inertial frame needs to be in a small spacetime region. Please edit it or write a new answer if it's not clear :-) – innisfree May 28 '13 at 17:24

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