Lovelock's theorem
= Lovelock's theorem
{c}
In four dimensions, a local natural symmetric divergence-free metric tensor involving the metric and its derivatives of at most second order has the Lovelock form $aG_{ab}+bg_{ab}$ with constant coefficients. Generic nonlinear metric <f(R) gravity> instead has fourth-order terms and does not meet that derivative-order hypothesis. For affine $f$, the metric field equation is precisely of Lovelock form.