Higher Dimensional Static and Spherically Symmetric Solutions in Extended Gauss–Bonnet Gravity
Abstract
We study a theory of gravity of the form $f(\mathcal{G})$ where $\mathcal{G}$ is the GaussBonnet topological invariant without considering the standard EinsteinHilbert 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 $f(\cal G)$ 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 GaussBonnet gravity is significant without assuming the Ricci scalar in the action.
 Publication:

Symmetry
 Pub Date:
 March 2020
 DOI:
 10.3390/sym12030372
 arXiv:
 arXiv:1911.03554
 Bibcode:
 2020Symm...12..372B
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory
 EPrint:
 10 pages