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Sean Carroll states the Einstein's Equivalence Principle (EEP) as "In small enough regions of spacetime, the laws of physics reduce to those of special relativity; it is impossible to detect the existence of a gravitational field by means of local experiments."

Local flatness theorem says that there exists a class of coordinate transformations such that any general metric can be brought into the Minkowskian form (special relativity form). So isn't a proof of the local flatness theorem is (almost) a proof of the EEP?

Qmechanic
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Sashwat Tanay
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    @0celo7 The problem is that if physicists were not allowed to do GR, GR would probably not exists. – fqq Nov 22 '17 at 23:50
  • Beautiful comment @ocel07 : I say this all the time! No one mentions that you have to ensure that the derivatives of the connection coefficients must vanish as well to have true flatness! Also, ask them to transfer away the non-diagonal component of the Kerr metric to Minkowski! – Dr. Ikjyot Singh Kohli Nov 23 '17 at 04:32

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