Is there a universal criteria to determine if a coordinate system is global?(adsbygoogle = window.adsbygoogle || []).push({});

I think that it is sufficient for the determinant of the metric to be non-zero in order for a coordinate system to be global. Is this so?

For example, take the metric

##ds^{2} = \ell^{2}(-\cosh^{2}\rho\ dt^{2} + d\rho^{2} + \sinh^{2}\rho\ d\phi^{2}).##

I'd say that this metric is not global because ##\sinh\rho = 0## for ##\rho = 0##. What do you think?

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# A Global coordinate system

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