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.
Highlights
General relativity (GR) is known to be the most successful theory for gravitational interactions so far
These are mostly related to the dark universe, i.e., the nature of dark energy and dark matter, as well as the inability to find a TeV scale supersymmetry, the nature of singularities, the value of the cosmological constant and other less important astrophysical problems [1,2]
We seek for the condition in order that the Lagrangian density (18) would admit any Noether symmetry which has a generator of the form
Summary
General relativity (GR) is known to be the most successful theory for gravitational interactions so far. We will study the invariance of the f ( R, G ) theory of gravity, which is a generalization of f ( R) theory containing a Gauss–Bonnet scalar in the arbitrary function, under point transformations in a spherically symmetric background. We will present those models that possess Noether symmetries, calculate their invariant functions and find exact spherical solutions in some of the cases.
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