I'm looking for recommendations for a good place that discusses at a basic level what physical length, time, simultaneity, etc. mean, for an arbitrary metric.(adsbygoogle = window.adsbygoogle || []).push({});

Landau does discuss this a bit, but in a way that confuses me -- for example he calls

[tex]\sqrt{g_{00}} dx^0[/tex]

"proper time", but in the SR limit this would just become dt, which isn't proper time, is it? Landau goes on to use this to derive distance in GR

[tex]\gamma_{ij} dx^i dx^j = \left( -g_{ij} + \frac{ g_{0i} g_{oj} }{g_{00}} \right) dx^i dx^j[/tex]

where my indices are spatial -- they run only from 1 to 3.

I'd like to understand where these expressions come from, and more importantly gain a good understanding of what length and time mean.

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# Length and time for a given metric

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