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- About the definition to use for a global inertial frame in GR

Hi,

starting from this thread Principle of relativity for proper accelerating frame of reference I'm convincing myself of some misunderstanding about what a global inertial frame should actually be.

In GR we take as

Now consider a finite region of spacetime outside the Earth: take a family of free-falling bodies (a geodesic congruence) foliating it: if we choose a frame (coordinate chart) in which those free-falling bodies are at rest (i.e. having constant spatial coordinates in that frame) then it should

What is wrong in the above claim ? (sure...I'm aware of global inertial frames actually do not exist in GR).

Thank you.

starting from this thread Principle of relativity for proper accelerating frame of reference I'm convincing myself of some misunderstanding about what a global inertial frame should actually be.

In GR we take as

*definition*of inertial frame (aka inertial coordinate system or inertial coordinate chart) the following:a frame (aka coordinate chart) is inertial -- bydefinition-- if accelerometers everywhere at rest in it measure zero proper acceleration.

Now consider a finite region of spacetime outside the Earth: take a family of free-falling bodies (a geodesic congruence) foliating it: if we choose a frame (coordinate chart) in which those free-falling bodies are at rest (i.e. having constant spatial coordinates in that frame) then it should

*match*the above definition of (global) inertial frame -- global at least for that finite region of spacetime.What is wrong in the above claim ? (sure...I'm aware of global inertial frames actually do not exist in GR).

Thank you.

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