Editing Einstein–Hilbert action (section)

===Equation of motion===
Now that we have all the necessary variations at our disposal, we can insert ({{EquationNote|3}}) and ({{EquationNote|4}}) into the equation of motion ({{EquationNote|2}}) for the metric field to obtain

{{NumBlk|:|<math>R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R = \frac{8 \pi G}{c^4} T_{\mu\nu}</math>,|{{EquationRef|5}}}}

which is the [[Einstein field equations]], and

:<math>\kappa = \frac{8\pi G}{c^4}</math>

has been chosen such that the non-relativistic limit yields [[Newton's law of universal gravitation|the usual form of Newton's gravity law]], where <math>G</math> is the [[gravitational constant]] (see [[Einstein field equations#The correspondence principle|here]] for details).