Exact Spherically Symmetric Solutions in Modified Gauss–Bonnet Gravity from Noether Symmetry Approach
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 GaussBonnet 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.
 Publication:

Symmetry
 Pub Date:
 January 2020
 DOI:
 10.3390/sym12010068
 arXiv:
 arXiv:1912.12922
 Bibcode:
 2020Symm...12...68B
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 17 pages. Accepted for Publication in Symmetries in the special issue "Noether's symmetry approach in gravity and cosmology"