I got some trouble from this question: For a given metric: ds2 =t-2(dx2-dt2), derive the energy-momentum tensor which satisfies the Einstein equation: Rαβ- 1/2Rgαβ=8[itex]\pi[/itex]GTαβ. 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!