# Gauss-Bonnet (GB) gravity The action of Gauss-Bonnet gravity is$S=\frac{1}{16 \pi G_N} \int d^{D} x \sqrt{-g}\left[R+\lambda_{G B}\left(R^2-4 R_{\mu \nu} R^{\mu \nu}+R_{\mu \nu \rho \sigma} R^{\mu \nu \rho \sigma}\right)\right],$where we have kept the usual [[0554 Einstein gravity|Einstein-Hilbert]] term. Depending on the context, the coupling $\lambda_{GB}$ can either be taken to be finite or infinitesimal. The GB term is topological in $D=4$, but non-trivial in higher dimensions. The theory is a special example of [[0006 Higher-derivative gravity|higher-derivative gravity]] theories because its equation of motion is second-order. In particular, it belongs to the [[0341 Lovelock gravity|Lovelock]] family, which is the most general pure higher-derivative gravity (i.e. no matter) that has a second-order equation of motion. ## Refs - reviews - [[2022#Fernandes, Carrilho, Clifton, Mulryne]] - spherically symmetric solution - independently by [[1985#Boulware, Deser]] and [[1986#Wheeler]] ## Amplitudes GB gravity is topological in 4D, so it does not have nontrivial amplitudes. ## Related topics - [[0341 Lovelock gravity]] - [[0015 Modified gravity]] - [[0006 Higher-derivative gravity]]