# Coordinate Transformations in GR

1. Dec 15, 2008

As I try to understand GR, I find coordinate transformations just about everywhere. My question is simply: What is the reason coordinate transformations play such an important role in GR? Thanks.

2. Dec 15, 2008

### GDogg

I'd say the reason is that one of the most important aspects of GR is the principle of relativity and the general covariance of its equations. Basically, that the laws of physics should be the same in any reference frame so naturally you'll want to perform coordinate trasnformations.

Last edited: Dec 15, 2008
3. Dec 15, 2008

### Crazy Tosser

That and also coordinate transformation is the simplest (read: best) way to visualize reference frames.

4. Dec 15, 2008

### atyy

In special relativity, you can can use 3 spatially orthogonal plane wave solutions of Maxwell's "free space" equations as rulers for 3 orthogonal spatial axes. The 3 rulers won't interact with each other and Maxwell's equations are linear. In general relativity, each plane wave has energy or "gravitational mass" and should attract the other plane waves, so Maxwell's "free space" equations should become nonlinear indicating that you cannot get independent plane wave solutions. This will be true of any rulers you set up, so you will have no orthogonal coordinates, except very locally. The bending of your rulers and clocks or "metric" appears as spacetime curvature.

5. Dec 15, 2008

### cesiumfrog

Another reason is that GR permits solutions in which it is mathematically impossible for a single choice of coordinates to fully suffice at every event.

6. Dec 30, 2008