Higher Dimensional Static and Spherically Symmetric Solutions in Extended Gauss–Bonnet Gravity - Francesco Bajardi (Symmetry, 2020)
We study a theory of gravity of the form <semantics> f ( G ) </semantics> where <semantics> G </semantics> is the Gauss−Bonnet topological invariant without considering the standard Einstein−Hilbert term as common in the literature, in arbitrary <semantics> ( d + 1 ) </semantics> dimensions. The approach is motivated by the fact that, in particular conditions, the Ricci curvature scalar can be easily recovered and then a pure <semantics> f ( G ) </semantics> gravity can be considered a further generalization of General Relativity like <semantics> f ( R ) </semantics> gravity. Searching for Noether symmetries, we specify the functional forms invariant under point transformations in a static and spherically symmetric spacetime and, with the help of these symmetries, we find exact solutions showing that Gauss−Bonnet gravity is significant without assuming the Ricci scalar in the action.