inertial structure is local. Thus far, an inertial reference frame has been something that can be defined for the whole Universe at once—but if inertial structure is determined by gravitational effects of matter, and if those effects vary from place to place, then inertial structure likewise must vary from place to place. The notion of a single collection of inertial frames is replaced by a patchwork, one collection for each little region of spacetime. This in turn requires us to set rules for how adjacent collections of frames are related to one another; these rules are what physicists mean
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inertial structure - local.
spacetime curvature
