Einstein field equations

Coming from Einstein--Hilbert action.
We have

R_{a b} - \frac{1}{2} g_{a b} R = 8 π G_{N} T_{μ ν}

$R_{a b}$ : Ricci curvature tensor
$R$ : Ricci scalar curvature

The left hand side comes from the "curvature part" of the Lagrangian, and the right hand side from the "matter part" of the Lagrangian.
If we add the cosmological constant to the Lagrangian we have

R_{a b} - \frac{1}{2} g_{a b} R + Λ g_{a b} = 8 π G_{N} T_{μ ν}

We can rename $R_{a b} - \frac{1}{2} g_{a b} R$ as the Einstein curvature tensor $G_{a b}$ , so we have:

G_{a b} + Λ g_{a b} = 8 π G_{N} T_{μ ν}