# Lovelock gravity Lovelock gravity is the most general [[0006 Higher-derivative gravity|higher-derivative gravity]] (with no matter) that has second-order equation of motion. ## Refs - parent topic: [[0006 Higher-derivative gravity]] - main refs - [[TeitelboimZanelli1987]] - [[Lovelock1970]] & [[Lovelock1971]] ## Significance - GB as the first order correction in $\alpha^\prime$ from string theory - [[Zwiebach1985]] using field redefinition ## Properties - equivalence between metric and Palatini formulations - [[ExirifardSheikh-Jabbari2007]] arXiv:0705.1879 - cosmic censorship - [[CamanhoEdelstein2013]][](https://arxiv.org/abs/1308.0304) ## Solutions - exact asymptotically flat BH - [[Wheeler1986b]]“Symmetric Solutions To The Gauss-Bonnet Extended Einstein Equations,” Nucl. Phys. B 268 (1986) 737; - [[Wheeler1986a]]“Symmetric Solutions To The Maximally Gauss-Bonnet Extended Einstein Equations,” Nucl. Phys. B 273 (1986) 732; - [[MyersSimon1988]] “Black Hole Thermodynamics in Lovelock Gravity,” Phys. Rev. D 38 (1988) 2434; [[MyersSimon1989]] “Black Hole Evaporation and Higher Derivative Gravity,” Gen. Rel. Grav. 21, 761 (1989) - asymptotically AdS BH - [[DeBoerKulaxiziParnachev2009]][](https://arxiv.org/abs/0912.1877) ## Boundary term - [[0138 Variational principle]] - [[Bunch1981]] “Surface terms in higher derivative gravity,” J. Phys. A: Math. Gen. 14 (1981) L139 - [[Myers1987]] “Higher Derivative Gravity, Surface Terms and String Theory,” Phys. Rev. D 36, 392 (1987) ## In 4D - [[0425 Gauss-Bonnet gravity|GB]] is topological in 4D - the Lagrangian is identically zero for the cubic Lovelock theory in 4D