Higher dimensional static and spherically symmetric solutions in extended Gauss-Bonnet gravity

TL;DR

This paper explores pure $f( ext{Gauss-Bonnet})$ gravity in higher dimensions, identifying exact static, spherically symmetric solutions through Noether symmetries, highlighting the importance of Gauss-Bonnet terms without Ricci scalar inclusion.

Contribution

It introduces a novel analysis of pure $f( ext{Gauss-Bonnet})$ gravity in arbitrary dimensions, deriving exact solutions via symmetry methods.

Findings

Exact static, spherically symmetric solutions found.

Gauss-Bonnet gravity is significant without Ricci scalar.

Noether symmetries help determine functional forms.

Abstract

We study a theory of gravity of the form $f(\mathcal{G})$ where $\mathcal{G}$ 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.