Exact spherically symmetric solutions in modified Gauss-Bonnet gravity from Noether symmetry approach

It is broadly known that Lie point symmetries and their subcase, Noether symmetries, can be used as a geometric criterion to select alternative theories of gravity. Here, we use Noether symmetries as a selection criterion to distinguish those models of $f(R,G)$ theory, with $R$ and $G$ being the Ricci and the Gauss-Bonnet scalars respectively, that are invariant under point transformations in a spherically symmetric background. In total, we find ten different forms of $f$ that present symmetries and calculate their invariant quantities, i.e Noether vector fields. Furthermore, we use these Noether symmetries to find exact spherically symmetric solutions in some of the models of $f(R,G)$ theory.