<p>Some desirable properties are that the coordinates of events are uniquely specified; that the coordinate system doesn't lead to singularities in the metric; and that the coordinates adequately span all the spacetime region of interest.</p>
<p>It is often not possible to satisfy all these conditions, which is why a variety of coordinate choices are often made.</p>

CC BY-SA 4.0
2021-12-23T20:51:17.437Z
2021-12-23T20:51:17.437Z
ProfRob
<p>I was reading <a href="https://arxiv.org/abs/gr-qc/0612176" rel="nofollow noreferrer">&quot;Natural Coordinate System in Curved Spacetime&quot; by Ying-Qui Gu</a>.  The first sentence of the abstract struck me (bold emphasis added by me):</p>
<blockquote>
<p>In this paper we establish a generally and globally <strong>valid coordinate
system</strong> in curved space-time with the simultaneous hypersurface
orthogonal to the time coordinate.</p>
</blockquote>
<p>Is there a generally accepted set of criteria to determine if a coordinate system is valid?  Are some coordinate systems invalid?</p>

CC BY-SA 4.0
2021-12-23T19:49:14.220Z
The "valid" should be read together with "globally". It's a coordinate system that is *globally valid*, in contrast to one that is only *locally valid*. But I think this question belong at physics.SE
pela
<coordinate><definition>
What is a "valid" coordinate system?
Connor Garcia
# What is a "valid" coordinate system?

(Asked by: username_0 on 2021-12-23)

I was reading ["Natural Coordinate System in Curved Spacetime" by Ying-Qui Gu](https://arxiv.org/abs/gr-qc/0612176). The first sentence of the abstract struck me (bold emphasis added by me):

> In this paper we establish a generally and globally **valid coordinate
> system** in curved space-time with the simultaneous hypersurface
> orthogonal to the time coordinate.

Is there a generally accepted set of criteria to determine if a coordinate system is valid? Are some coordinate systems invalid?

**Tags:** coordinate, definition
> **Comments:**
> **username_1**: The "valid" should be read together with "globally". It's a coordinate system that is *globally valid*, in contrast to one that is only *locally valid*. But I think this question belong at physics.SE  

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## 1 answers

### Answer by username_2 on 2021-12-23. Score: 1

Some desirable properties are that the coordinates of events are uniquely specified; that the coordinate system doesn't lead to singularities in the metric; and that the coordinates adequately span all the spacetime region of interest.

It is often not possible to satisfy all these conditions, which is why a variety of coordinate choices are often made.


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