= Newtonian normalization of the Einstein field equations
{c}
{title2=$G_{ab}+\Lambda g_{ab}=\kappa T_{ab}$}
Assume a metric theory in four dimensions, a <Levi-Civita connection>, covariant <stress-energy conservation> and field equations linear in second metric derivatives. The <contracted Bianchi identity> selects $G_{ab}=R_{ab}-g_{ab}R/2$. Its trace-reversed equation is $R_{ab}=\kappa(T_{ab}-g_{ab}T/2)+\Lambda g_{ab}$. In the convention $R_{00}\simeq-\nabla^2\varphi$ and signature $(+---)$, nonrelativistic matter gives $R_{00}\simeq\kappa\rho/2$. The <Poisson equation> $\nabla^2\varphi=4\pi G\rho$ fixes $\kappa=-8\pi G$. Reversing the curvature convention reverses this displayed coupling sign without changing the physical theory. The <strong equivalence principle> alone does not establish uniqueness without the stated additional assumptions.
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