I'm reading Spacetime and Geometry: An Introduction to General Relativity by Sean M. Carrol and in the chapter on gravitation, he derives the Einstein Field Equations. Here is the part I don't get. He starts with the equation [tex]R_{\mu\nu}-\frac{1}{2} Rg_{\mu\nu}=\kappa T_{\mu\nu}[/tex] Wher [itex]R_{\mu\nu}[/itex] is the Ricci tensor, [itex]\kappa[/itex] is some constant, and [itex]T_{\mu\nu}[/itex] is the stress-energy tensor. Then he sates that by contracting both sides it becomes,[tex]R=-\kappa T[/tex] where [itex]R=R_{\mu\nu}g^{\mu\nu}[/itex] and [itex]T=T_{\mu\nu}g^{\mu\nu}[/itex]. I don't see how he came to this answer. When I tried to work it out myself I got [tex]R=2\kappa T[/tex] This obviously isn't the right answer, and I can't see what I'm missing. I'm drawing a blank here.(adsbygoogle = window.adsbygoogle || []).push({});

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# Derivation of Einstein Field Equations

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