Rest Frame in GTR: What Is It?

[Sandeep T S]

In STR we measure motion relative to a observer, and the he is rest respect to him. We make coordinates relative to "a rest frame" , that is the observer.
In GTR ,all motion are calculated from which frame?

 

[Ibix]

Any you like. That you have a free choice is basically what the word "relativity" means in this context.

Note that this is also true in special relativity - it is usually formulated in terms of global inertial reference frames because that's easier, but it's not obligatory.

Note also that it isn't always possible to use one single coordinate system to cover all of a curved spacetime.

Finally, note that there is often a particular coordinate system picked out by the physics you're interested in. Maths is often easier using this system. For example Schwarzschild's coordinates in Schwarzschild spacetime are convenient for observers stationary with respect to the black hole and co-moving coordinates are convenient for cosmology. Nothing stops you using more weird and wonderful systems if you like, except the headaches and extra algebra doing so induces.

 

[pervect]

In STR we measure motion relative to a observer, and the he is rest respect to him. We make coordinates relative to "a rest frame" , that is the observer.
In GTR ,all motion are calculated from which frame?

In introductory SR, inertial frames of reference are usually specified These inertial frames must have certain properties and follow certain conventions for the theory to work. GR allows the use of generalized coordinates, that have no other requirements than smoothness, uniqueness, and internal consistency. (This may not be a complete list of the modest requirements for coordinates in GR and it is off-the-cuff rather than mathematically precise).

The use of generalized coordinates is not actually unique to GR, SR can also use general coordinates, via the use of tensors. The necessary tensor methods are usually taught at the graduate level (though sometimes advanced undergraduate levels).

Some authors, (for instance Misner, in "Precis of General Relativity") advocate omitting the concept of an observer from GR entirely as unnecessary. I would tend to agree that it's not necessary or even particularly useful to talk about observers at an introductory level, but it can be convenient later on.

Finding one's coordinates in GR is rather like locating oneself on a map of the Earth. Certain landmarks on the map are specified, and one observes these landmarks by taking physical measurements, such as telescope observation times and bearings (in the case of astronomy), or by receiving radio transmisions from satellites (in the case of GPS). From these observations of these reference landmarks, combined with the map of space-time, one is able to locate oneself on the space-time map, finding one's position in space, and one's "position in time", i.e. one's time coordinate.

Given a set of coordinates, one can single out the worldlines of objects with constant coordinates, which one could measure motion relative to.

The mathematical entity that serves as the "map" in GR is the metric tensor. It's usually presented as a mathematical formula. Learning about GR generally consists of first learning what a tensor is, followed by learning what the metric tensor is. The last phase is learning how to manipulate the metric tensor to calculate the other mathematical entities in the theory (curvature tensors, Christoffel symbols, geodesic paths, for instance, all of which can be calculated from a knowledge of the metric tensor). Finally, to intererpret the theory, one needs to connect the math to the previously mentioned physical observations.

 

[A.T.]

We make coordinates relative to "a rest frame" , that is the observer.

In the context of Relativity "observer" is usually just a synonym for "reference frame". However, to define a reference frame, you don't need an actual physical observer at rest in that frame. So this language is misleading.