GR: Local Inertial Frame & Poincare Invariance

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SUMMARY

The discussion centers on the possibility of defining a local inertial frame that is Poincaré invariant within the context of general relativity. It is established that every manifold is locally flat, allowing for the selection of coordinates that approximate pseudoeuclidean structures. However, the existence of truly inertial frames in non-flat spacetimes is negated unless one considers frames that are approximately inertial or valid for infinitesimal regions. Furthermore, there is currently no solution for a curved, static spacetime that encompasses a Riemann flat 4D hypervolume extending beyond a point.

PREREQUISITES
  • Understanding of general relativity principles
  • Familiarity with local inertial frames
  • Knowledge of Poincaré invariance
  • Concept of Riemann flat spaces
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  • Research the implications of local inertial frames in general relativity
  • Study the concept of Poincaré invariance in curved spacetimes
  • Explore Riemannian geometry and its applications in physics
  • Investigate the characteristics of static spacetimes in general relativity
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The discussion is beneficial for theoretical physicists, mathematicians specializing in geometry, and students studying general relativity and its implications in modern physics.

paweld
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Is it possible to deifine local inertial frame which is Poincare invariant (in general relativity)
(every manifold is locally flat, so we can chose coordinates which are
almost pseudoeuclidean, but in what sense they might be Poincare invariant)
Thanks.
 
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paweld said:
Is it possible to deifine local inertial frame which is Poincare invariant (in general relativity)
(every manifold is locally flat, so we can chose coordinates which are
almost pseudoeuclidean, but in what sense they might be Poincare invariant)
Thanks.
That hinges on how you want to define local.

Strictly speaking in a non-flat spacetime there are no inertial frames unless you consider a frame inertial when the frame is approximately inertial or when the frame is valid for the size of a point.

As far as I know there is no solution for a curved and necessarily static spacetime that contains a region with a Riemann flat 4D hypervolume extending the 'size' of a point.
 

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