2019/11/08 by Bajardi, Francesco, Dialektopoulos, Konstantinos F., Capozziello, Salvatore
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.1911.03554
We study a theory of gravity of the form f(G) where G is the Gauss-Bonnet topological invariant without considering the standard Einstein-Hilbert term as common in the literature, in arbitrary (d+1) dimensions. The approach is motivated by the fact that, in particular conditions, the Ricci curvature scalar can be easily recovered and then a pure f(\cal G) gravity can be considered a further generalization of General Relativity like f(R) 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.