# Lorentz transformations in non-inertial frames

Do you know how can we derive these local transformations for accelerated frames? I think, as a rule this thema does not even come up with the introduction of GR! The paper, that Demystifier posted, is the only one I've seen, which handles relativistic corrections for rotational movement ( and of course concurs with the ordinary SR boosts for ω=0 ).

For istance, d'Inverno's textbook instructs as about how to solve the geodesic equations in comoving coordinate systems even in flat spacetime but does not mention anything about their transformations. The same holds for Carroll's notes, where the fact that SR can handle accelerations is mentioned ( as once @DaleSpam pointed out in another thread :) ), but there are no explicit maths given! The list goes on...

Moreover it is crucial to emphasize that coordinate transformations do depend on the relativity of the frames. That means, if every coordinate system is equivalent, one must distinguish only between inertial and non-inertial frames to calculate the generalized transformations. To me, the transformation from an accelerated to an accelerated frame would be different from the transformation from an accelerated to an inertial and so on and so forth.

Ok I finally found some well documented relations...
http://www.imcce.fr/hosted_sites/tempsespace/archives/seminTE-14-06-2010.pdf [Broken]

But unlike the Lorentz transformations, they lack a beautiful matrix representation... Fpr instance I do no see how we could write the velocity transformation (eq 2) covariantly...

I am impressed/confused by the fact that, accelerating frames in curved spacetime can be described covariantly, whilst their treatment in flat spacetime is so complicated... I am not sure anymore even if GR treats accelerating (due to some force) local frames after all..

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