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Higher Dimensional Static and Spherically Symmetric Solutions in Extended Gauss–Bonnet Gravity
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In: Symmetry ; Volume 12 ; Issue 3 (2020)
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Abstract:
We study a theory of gravity of the form f ( G ) where G is the Gauss&ndash ; Bonnet topological invariant without considering the standard Einstein&ndash ; 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&ndash ; Bonnet gravity is significant without assuming the Ricci scalar in the action.
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Keyword:
alternative theories of gravity; Gauss–Bonnet invariant; solar system tests; spherical symmetry
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URL: https://doi.org/10.3390/sym12030372
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