Einstein–Hilbert action
The Einstein–Hilbert action in general relativity yields the Einstein field equations through the principle of stationary action. With the ( − , + , + , + ) {\displaystyle (-,+,+,+)} metric signature, the gravitational part of the action is given as S = 1 2 κ ∫ R − g d 4 x , {\displaystyle S={1 \over 2\kappa }\int R{\sqrt {-g}}\,\mathrm {d} ^{4}x,} where g = det ( g μ ν ) {\displaystyle g=\det(g_{\mu \nu })} is the determinant of the metric tensor matrix, R {\displaystyle R} is the Ricci scalar, and κ = 8 π G c − 4 {\displaystyle \kappa =8\pi Gc^{-4}} is the Einstein gravitational constant, G {\displaystyle G} is the gravitational constant and c {\displaystyle c} is the speed of light in vacuum.