In SR there is a whole family of so called inertial observers that are defined as those observers that move at relative constant speed with respect to one another, whose descriptions of nature are all equivalent and whose spacetime coordinate are related by Lorentz transformations i.e. those transformations that leave the interval between any two events invariant. A frame of reference is naturally associated with an observer: we can imagine the observer at the origin and a frame of synchronized clocks and rigid rods that fills all of space, comoving with the observer.(adsbygoogle = window.adsbygoogle || []).push({});

In GR spacetime is some general manifold and so it may be impossible to set up coordinates everywhere. Locally, however, we can find coordinates that make the neighbourhood of an event diffeomorphic to R4. Different coordinate charts are possible, as long as they are smoothly related to each other. The physics doesn't depend on the chart, we can choose whatever coordinates we like. Also, these coordinates are not always easy to understand physically. For example, the t coordinate not always corresponds to the time measured by a real clock. The interpretation depends on the specific form the metric takes in the coordinates chosen.

This is the abstract talk. Now, where is the observer in GR? Is the observer associated with a chart? But then how are observers related 'kinematically'? By that I mean: in SR there is a clear physical parameter, the relative velocity, that enters into the coordinates transformation between two observers, but in GR how can we 'translate' the description of one observer in the description of another? For example, a Schwarzchild BH. In the usual Schwarzchild coordinates t is the time measured by an observer at infinity, so these are the coordinates 'natural' for him. Another observer is freely falling towards the BH. Whate are the coordinates natural for him? How can I, distant observer, know what he experiences or measures? Are these two observers'equivalent'? One lives practically in Minkowski space and the other is freely falling, so they should be. Or not? And what happens at the horizon? To sum it up, in SR we can answer this sort of question because we know explicitly how our coordinates are related to the coordinates of another observer and these coordinates are directly related to physical observables, like time intervals or space lenghts, but in GR?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Concept of coordinate reference frame in GR

Loading...

Similar Threads - Concept coordinate reference | Date |
---|---|

B Why do we need the concept of "event" in SR | Jun 15, 2017 |

I Concept q -- affine parameter and coordinate time geodesic | Jan 30, 2017 |

I Why was time dilation under GR a new concept? | Dec 19, 2016 |

Simultaneity in General Relativity and Problem with coordinate systems concepts. | Mar 27, 2011 |

**Physics Forums - The Fusion of Science and Community**