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## Main Question or Discussion Point

I can understand that a free falling frame in a curved space with a non-zero Riemann tensor has a zero Ricci tensor but I have a doubt about the opposite; does an accelerating frame in a vacuum space have a non-zero Ricci or Riemann tensor? if so, where do components of energy momentum tensor come from then?

Also what is the law of general transformation between the curved space-time and the flat space-time in a free-falling inertial frame?

Also what is the law of general transformation between the curved space-time and the flat space-time in a free-falling inertial frame?