Normalization of the metric f(R) field equation
= Normalization of the metric f(R) field equation
{title2=$A E_{ab}=\frac12T_{ab}$}
For a metric action $S_g=A\int\sqrt{-g}f(R)\,d^4x$ and the usual <stress-energy tensor> convention, covariant metric variation gives $A E_{ab}=T_{ab}/2$, where $E_{ab}=f'R_{ab}-fg_{ab}/2+(g_{ab}\Box-\nabla_a\nabla_b)f'$. With $A=1/(16\pi G)$ this becomes $E_{ab}=8\pi G T_{ab}$; with $A=1$ it becomes $E_{ab}=T_{ab}/2$. The chosen normalization does not alter the vacuum equation.