Transformations in curved spacetime?

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1. Mar 1, 2014

wpan

I know that the spacetime in special relativity is not curved and that the axis can be transformed via the lorentz transformations.

I was wondering if the curved spacetime in general relativity can be transformed in such a way, and if so, how?

2. Mar 2, 2014

dauto

Yes of course. The Lorentz transformations are the set of transformations that preserve the space-time interval $$ds^2 = dt^2 - dx^2 - dy^2 - dz^2$$. A similar concept of space-time interval also applies to GR.

3. Mar 2, 2014

Naty1

Depends on just what you mean, but generally, 'no'.

Wikipedia puts it this way: [Minkowski space is the the flat space-time of SR]
http://en.wikipedia.org/wiki/Lorentz_transformation

In the flat spacetime of SR the space-time separation between two events or two observers is the integral of ds along a straight line from one event to the other. [There is only one such straight line.] The analogous measure in curved spacetime would be the integral of ds along a geodesic [free fall path], generally a curved worldine. But in general in curved spacetime there are multiple geodesics connecting the events so you won't see much talk of “space-time separation” in GR because there are many such paths.

Last edited: Mar 2, 2014