. Thus we conclude that Equation of motion Now that we have all the necessary variations at our disposal, we can insert () and () into the equation of motion () for the metric field to obtain which is the Einstein field equations, and has been chosen such that the non-relativistic limit yields the usual form of Newton's gravity law, where is the gravitational constant (see here for details). Cosmological constant When a cosmological constant Λ is included in the Lagrangian, the action: Taking variations with respect to the inverse metric: Using the action principle: Combining this expression with the results obtained before: We can obtain: With , the expression becomes the field equations with a cosmological constant: See also Belinfante–Rosenfeld tensor Brans–Dicke theory (in which the constant k is replaced by a scalar field). Einstein–Cartan theory f(R) gravity (in which the Ricci scalar is replaced by a function of the Ricci curvature) Gibbons–Hawking–York boundary term Kaluza–Klein theory Komar superpotential Palatini action Teleparallelism Tetradic Palatini action Variational methods in general relativity Vermeil's theorem Notes Bibliography Hilbert, D. (1915) Die Grundlagen der Physik (German original for free) (English translation for $25), Konigl. Gesell. d. Wiss. Göttingen, Nachr. Math.-Phys. Kl. 395-407 Christopher M. Hirata Lecture 33: Lagrangian formulation of GR (27 April 2012). Variational formalism of general relativity General relativity Albert Einstein Gravity David Hilbert