in a sufficiently small region of spacetime such that the Christoffel symbols vanish at a point.

Spacetime curvature, however, represents an intrinsic geometric property of spacetime associated with tidal effects and geodesic deviation. Unlike Christoffel symbols, curvature cannot generally be transformed away even locally by a change of coordinates. Even in a freely falling frame where local gravitational effects disappear, nearby freely falling particles may still accelerate relative to one another because of spacetime curvature.

Thus,

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