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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Metric tensor and spacetime

**Physics Forums | Science Articles, Homework Help, Discussion**