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Einstein's Equations are usually written ##R_{\mu\nu}-(1/2)g_{\mu\nu}R={\kappa}T_{\mu\nu}## , where ##\kappa## is a constant. If you were to multiply both sides by ##g^{\mu\nu}## , then this becomes ##R=-{\kappa}g^{\mu\nu}T_{\mu\nu}## . I have used the relations ##g^{\mu\nu}g_{\mu\nu}=4## and ##R=g^{\mu\nu}R_{\mu\nu}## . ##g^{\mu\nu}T_{\mu\nu}## is the trace of the Stress Energy Tensor, which now leaves you with ##R=-{\kappa}T^{\mu}_{\mu}## . It seems to me that writing the Einstein Field Equations this way simplifies them, but I've never seen them written this way. Have I done something wrong using this approach, or is it not practical to write them in this form? Thank you for any explanation :).