I got some trouble from this question:(adsbygoogle = window.adsbygoogle || []).push({});

For a given metric: ds^{2}=t^{-2}(dx^{2}-dt^{2}), derive the energy-momentum tensor which satisfies the Einstein equation: R_{αβ}- 1/2Rg_{αβ}=8[itex]\pi[/itex]GT_{αβ}.

I got the Ricci scalar R=2, but Tαβ=0 for all α,β. Does this means a curved spacetime without any source(energy-momentum tensor)? Is this possible? Or this result implies that I have made some mistakes in my calculation?

Thanks for answering this question!

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# A question of Einstein field equation

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