Reference frame vs coordinate system

[PeterDonis]

I take it as if we assign fixed spatial coordinate values to observer's parts (i.e. to their worldlines in the worldtube) and define coordinate time such that the Pythagorean theorem holds for the proper distance of events at rest in the chart being defined that have the same coordinate time value (i.e. they are Einstein synchronized).

You can't do that if geodesic deviation is present. If geodesic deviation is present, one of the elements of your prescription must fail. It is impossible to meet all of your requirements in the presence of geodesic deviation.

 

[lriuui0x0]

I found some new reference on this. In book "Special Relativity in General Frame", the concept of "local frame" is defined, similarly the concept of observer, in section 3.4.

I wonder if this is a common definition, and does it generalise to GR well?

 

[PeterDonis]

In book "Special Relativity in General Frame"

Can you give a link?

 

[PeterDonis]

I wonder if this is a common definition, and does it generalise to GR well?

Yes and yes. The only thing missing from what you posted is that, to be a full frame field (i.e., tetrad field), the "local frame" needs to be defined, not just on the worldline, but in an open neighborhood around it. That enables the kinematic decomposition to be computed.

 

[lriuui0x0]

Can you give a link?

It's this book https://link.springer.com/book/10.1007/978-3-642-37276-6