Lovelock's theorem
Lovelock's theorem of general relativity says that from a local gravitational action which contains only second derivatives of the four-dimensional spacetime metric, then the only possible equations of motion are the Einstein field equations. The theorem was described by British physicist David Lovelock in 1971. Statement. In four dimensional space, any tensor formula_1 whose components are function of metric tensor formula_2 and its first and second derivatives (but linear in the second derivatives of formula_2), and also symmetric and divergenceless, then field equation in vacuum formula_4, then only possible form of formula_1 is where formula_7  and formula_8 are just simple constant numbers and formula_9 is the Einstein tensor. The only possible second-order Euler–Lagrange expression obtainable in a four-dimensional space from a scalar density of the form formula_10 is formula_11 Consequences. Lovelock's theorem means that if we want to modify the Einstein field equations, then we have five options.