= Trace-reversed stress-energy tensor
{title2=$\overline T_{\mu\nu}=T_{\mu\nu}-\tfrac12g_{\mu\nu}T$}
In four spacetime dimensions, the trace reversal of a <stress-energy tensor> has the displayed form, where $T=g^{\mu\nu}T_{\mu\nu}$. Its <trace> is $-T$, so applying trace reversal twice returns the original <tensor>. Taking the <trace> of the <Einstein field equations> without a cosmological constant gives $R=-\kappa T$; substitution yields $R_{\mu\nu}=\kappa\overline T_{\mu\nu}$. In a general dimension $d>2$, solving for the <Ricci tensor> instead uses $T_{\mu\nu}-g_{\mu\nu}T/(d-2)$.
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