GR: Local Inertial Frame & Poincare Invariance

[paweld]

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.

 

[Passionflower]

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.