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Exact Spherically Symmetric Solutions in Modified Gauss–Bonnet Gravity from Noether Symmetry Approach
Article

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

1
Department of Physics “E. Pancini”, University of Naples “Federico II”, 80138 Naples, Italy
2
INFN Sez. di Napoli, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126 Napoli, Italy
3
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, Yangzhou 225009, China
4
Gran Sasso Science Institute, viale F. Crispi 7, I-67100 L’Aquila, Italy
5
Physics Department, Tomsk State Pedagogical University, ul. Kievskaya, 60, Tomsk 634061, Russia
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(3), 372; https://doi.org/10.3390/sym12030372
Received: 10 January 2020 / Revised: 29 January 2020 / Accepted: 4 February 2020 / Published: 2 March 2020
(This article belongs to the Special Issue Noether’s Symmetry Approach in Gravity and Cosmology)
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. View Full-Text
Keywords: alternative theories of gravity; Gauss–Bonnet invariant; spherical symmetry; solar system tests alternative theories of gravity; Gauss–Bonnet invariant; spherical symmetry; solar system tests
MDPI and ACS Style

Bajardi, F.; Dialektopoulos, K.F.; Capozziello, S. Higher Dimensional Static and Spherically Symmetric Solutions in Extended Gauss–Bonnet Gravity. Symmetry 2020, 12, 372. https://doi.org/10.3390/sym12030372

AMA Style

Bajardi F, Dialektopoulos KF, Capozziello S. Higher Dimensional Static and Spherically Symmetric Solutions in Extended Gauss–Bonnet Gravity. Symmetry. 2020; 12(3):372. https://doi.org/10.3390/sym12030372

Chicago/Turabian Style

Bajardi, Francesco, Konstantinos F. Dialektopoulos, and Salvatore Capozziello. 2020. "Higher Dimensional Static and Spherically Symmetric Solutions in Extended Gauss–Bonnet Gravity" Symmetry 12, no. 3: 372. https://doi.org/10.3390/sym12030372

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