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This is a problem that is solved in my course notes, but I don't follow how it's done.

The problem is to find the general solution to Einstein's equations for a Robertson-Walker cosmology with a stress-energy tensor corresponding to the fluctuations of the void in QFT. This only means that [tex]T_{\mu\nu}=\Lambda g_{\mu\nu}[/tex] where lambda is a scalar.

So it start with

[tex]G_{\mu\nu}=8\pi GT_{\mu\nu}[/tex]

[tex]R_{\mu\nu}-\frac{1}{2}g_{\mu\nu}R=8\pi G \Lambda g_{\mu\nu}[/tex]

And then the next line is

[tex]R_{\mu\nu}=8\pi G(\Lambda - \frac{1}{2}g_{\mu\nu}T^{\lambda}_{\lambda})[/tex]

Since when is

[tex]R=-8\pi GT^{\lambda}_{\lambda}[/tex]

???

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# Homework Help: Gen. Rel. - Simple tensor stuff

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