we obtain the second field equation. Note that, unlike for the General Relativity field equations, the term does not vanish, as the result is not a total derivative. It can be shown that To prove this result, use By evaluating the s in Riemann normal coordinates, 6 individual terms vanish. 6 further terms combine when manipulated using Stokes' theorem to provide the desired . For comparison, the Lagrangian defining general relativity is Varying the gravitational term with respect to gives the vacuum Einstein field equation. In both theories, the full field equations can be obtained by variations of the full Lagrangian. See also Classical theories of gravitation Dilaton General relativity Mach's principle Scientific importance of GW170817 Notes References See Box 39.1. External links Scholarpedia article on the subject by Carl H. Brans Theories of gravity