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

TL;DR

This paper uses Noether symmetries to identify and derive exact spherically symmetric solutions in modified Gauss-Bonnet gravity models, enhancing understanding of their geometric and physical properties.

Contribution

It systematically finds symmetry-invariant $f(R,G)$ models and derives exact solutions, advancing the application of Noether symmetry methods in modified gravity theories.

Findings

Identified ten $f(R,G)$ models with Noether symmetries.

Derived exact spherically symmetric solutions for some models.

Provided invariant quantities and symmetry vectors for these models.

Abstract

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.