Does gravity as a fictitious force do work? (GR's free-falling frame POV)?

  • #76
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... only in flat spacetime is it true that every inertial observer can view himself at rest in a coordinate system with time-independent metric components.
After clarifying what it means, certainly different to my initial interpretation, I agree with this statement that it is actually simply the fact that only in curved spacetime can one measure tidal acceleration.
This is due to the non-uniform nature of gravitationl fields. That is why usually the Equivalence principle stresses the fact that the equivalence is local: In GR spacetime is equivalent to flat spacetime only locally (infinitesimally), evidently.
 
  • #77
PeterDonis
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It is true that one thing that distinguishes a time-independent (like Schwarzschild's) from a time dependent (like FRW) spacetime is precisely the fact that in the time-independent one can define a "static observer".
Yes, although instead of "time-independent spacetime" I would say "spacetime with a timelike Killing vector field". That's the key difference between the two, and it's a coordinate-free statement.
 

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