Hi guys. I'm taking a GR course right now, my first one. I was reading the textbook and I was wondering if you guys could help me out just to make sure I'm getting things straight here. I'm reading about the metric tensor, and I'm pretty sure I am expected to know what the metric tensor for a given spacetime is, if the line element if given to me. So, say we have this line element:(adsbygoogle = window.adsbygoogle || []).push({});

ds^{2}=e^{v(r)}dt^{2}-e^{[tex]\lambda[/tex](r)}dr^{2}-r^{2}(d[tex]\theta[/tex]^{2}+sin^{2}[tex]\theta[/tex]d[tex]\phi[/tex]^{2})

Is the metric tensor simply the coefficients of each differential arranged in the diagonal of a matrix, with the rest of the elements in it equal to zero? Or am I way off here?

NOTE: The Thetas and the phi in the expression are not supposed to be exponentials, I don't know why they came out that way.

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# Metric tensor and spacetime

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