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 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.
- Publication:
-
Symmetry
- Pub Date:
- January 2020
- DOI:
- 10.3390/sym12010068
- arXiv:
- arXiv:1912.12922
- Bibcode:
- 2020Symm...12...68B
- Keywords:
-
- Noether symmetry;
- exact solutions;
- spherical symmetry;
- Gauss-Bonnet;
- 04.30;
- 04.30.Nk;
- 04.50.+h;
- 98.70.Vc;
- General Relativity and Quantum Cosmology
- E-Print:
- 17 pages. Accepted for Publication in Symmetries in the special issue "Noether's symmetry approach in gravity and cosmology"