I need to write Schwarzschild Metric, that is in spherical coordinates, into the form that has the metric tensor.(adsbygoogle = window.adsbygoogle || []).push({});

Now, if the first the term of the metric is:

[tex]\Large (ds)^2=f(r)c^2dt^2-....[/tex] and x^{0}=ct,

then the first component g_{ij}of the metric tensor g is supposed to be:

[tex]\Large <\frac{\partial}{\partial x^i} \ | \ \frac{\partial}{\partial x^j}> \ ,i=j=0 \Rightarrow

(\frac{d}{dx^0}f(r)c^2dt^2 | \frac{d}{dx^0}f(r)c^2dt^2)[/tex]

But I do not actually understand that last statement. I guess dx^{0}=cdt, but I do not know how to proceed from that.

So I know this: the component g_{00}of g is supposed to be f(r), and I know that f(r) should come from the inner product, but I do not understand how. Basically, what does [tex]\Large \frac{d}{dx^0}f(r)c^2dt^2[/tex] mean?

I apologize if this should have been in the introductory section, or in the calculus section.

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# About Schwarzschild Metric

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