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I'm reading An Intro to GR, Hughston and Tod, it says that in GR the idea is that the geometry of st varies from point to point, represented by allowing the metric to vary over space-time.

It uses a (+,-,-,-) signature and so ##proper time=ds^{2}##.

It then makes the comment that proper time depends on the the observers location (compared to SR where it doesn't).

My question:

I believe it is always the case that the comtponents of a metric in GR are functions of space-time, and so I understand that proper time will vary for observers dependent upon location, but,

In flat space am I correct in thinking that the components also can depend upon space-time, e.g use of polar coordinates, and the

So from the above statement I would conclude that proper time also varies from location to location in SR. So shouldnt the statement instead be that

Thanks

It uses a (+,-,-,-) signature and so ##proper time=ds^{2}##.

It then makes the comment that proper time depends on the the observers location (compared to SR where it doesn't).

My question:

I believe it is always the case that the comtponents of a metric in GR are functions of space-time, and so I understand that proper time will vary for observers dependent upon location, but,

In flat space am I correct in thinking that the components also can depend upon space-time, e.g use of polar coordinates, and the

**only**case where it doesnt is cartesian coordinates?So from the above statement I would conclude that proper time also varies from location to location in SR. So shouldnt the statement instead be that

**if there does not exist coordinate system in which the components of the metric are not functions of space-time, the space-time is curved**from which it follows that proper time is location dependent.Thanks

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