Quantum gravity

Physics

Gravitation

Spacetime

Mathematics

Mathematical physics

Lagrangian

Scalar curvature

f(R) gravity

Ricci curvature

General relativity

Gauss–Bonnet theorem

Einstein

Curvature

Geometry

Gauss–Bonnet gravity

Quantum mechanics

Noether's theorem

Homogeneous space

Scalar (mathematics)

Classical mechanics

Quantum

Symmetry

We study a theory of gravity of the form f ( G ) where G is the Gauss–Bonnet topological invariant without considering the standard Einstein–Hilbert term as common in the literature, in arbitrary ( d + 1 ) dimensions. The approach is motivated by the fact that, in particular conditions, the Ricci curvature scalar can be easily recovered and then a pure f ( G ) gravity can be considered a further generalization of General Relativity like f ( R ) gravity. Searching for Noether symmetries, we specify the functional forms invariant under point transformations in a static and spherically symmetric spacetime and, with the help of these symmetries, we find exact solutions showing that Gauss–Bonnet gravity is significant without assuming the Ricci scalar in the action.

Higher Dimensional Static and Spherically Symmetric Solutions in Extended Gauss–Bonnet Gravity