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.

arXiv comment17 pages. Accepted for Publication in Symmetries in the special issue "Noether's symmetry approach in gravity and cosmology"

References in corpus (28)

• A Large Mass Hierarchy from a Small Extra Dimension
• f(R) Theories Of Gravity
• Modified Gravity and Cosmology
• 4D Gravity on a Brane in 5D Minkowski Space
• Extended Theories of Gravity
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Pre-Big-Bang in String Cosmology
• The Cosmology of Generalized Modified Gravity Models
• Teleparallel Theories of Gravity: Illuminating a Fully Invariant Approach
• Spherically symmetric solutions in f(R)-gravity via Noether Symmetry Approach
• Dark matter as a geometric effect in f(R) gravity
• Effects of the interaction between dark energy and dark matter on cosmological parameters
• Interacting Dark Energy and Dark Matter: observational Constraints from Cosmological Parameters
• Noether Symmetry Approach in $f(T,B)$ teleparallel cosmology
• New classes of modified teleparallel gravity models
• Noether symmetries in Symmetric Teleparallel Cosmology
• Dynamics of Inflation and Dark Energy from $F(R,\mathcal{G})$ Gravity
• Noether Symmetry Approach in Gauss-Bonnet Cosmology
• Noether Symmetries in Gauss-Bonnet-teleparallel cosmology
• Noether Symmetries as a geometric criterion to select theories of gravity
• Constraining Generalized Non-local Cosmology from Noether Symmetries
• Classification of the Horndeski cosmologies via Noether Symmetries
• Cartan symmetries and global dynamical systems analysis in a higher-order modified teleparallel theory
• Exact Spherically Symmetric Solutions in Modified Teleparallel gravity
• New Exact Spherically Symmetric Solutions in $f(R,\varphi ,X)$ gravity by Noether's symmetry approach
• Generalised teleparallel quintom dark energy non-minimally coupled with the scalar torsion and a boundary term
• Noether symmetries and boundary terms in extended Teleparallel gravity cosmology
• Topological invariant quintessence

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• Minisuperspace quantum cosmology in $f(Q)$ gravity
• Late-time constraints on modified Gauss-Bonnet cosmology
• Stellar Structures in $f(\mathcal{G})$ Gravity Admitting Noether Symmetries
• Cosmological perturbations in f(G) gravity
• How a conformally flat (GR)4 impacts Gauss-Bonnet gravity?
• The Noether Symmetry Approach: Foundation and applications. The case of scalar-tensor Gauss-Bonnet gravity
• On Dark Matter As A Geometric Effect in the Galactic Halo
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