On Coordinate Frames in Axisymmetric Static Vacuum Spacetimes and Implications for Observations

TL;DR

This paper examines how different coordinate choices in static axisymmetric vacuum spacetimes influence local observations, especially the effective potential and rotation curves, emphasizing the importance of coordinate selection in relativistic analysis.

Contribution

It highlights the significance of coordinate choice on physical observations and provides insights into the implications for interpreting relativistic phenomena.

Findings

Effective potential depends on the coordinate system used.

Rotation curves vary with different line element choices.

Coordinate frames influence the interpretation of local observations.

Abstract

While a physical theory should be independent of the coordinate frame chosen by any observer, the observations themselves in fact depend on the choice of coordinates. In particular, different coordinate frames reflect different symmetries seen by a local observer. In this work, we discuss the applicability of different coordinate choices and the resulting line elements for static axisymmetric vacuum spacetimes. We find that the effective potential experienced by a local observer in the low-velocity limit is highly dependent on the form of the line element and thus on the coordinates chosen in the description. For example, this affects the form of a rotation curve expected by such an observer. We thus conclude that it is important to review the choices of local (coordinate frame of the observer) and global symmetries carefully to understand observations from a generally relativistic point of view.