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Exact Spherically Symmetric Solutions in Modified Teleparallel Gravity
Open AccessArticle

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

1
Laboratory of Theoretical Physics, Institute of Physics, University of Tartu, W. Ostwaldi 1, 50411 Tartu, Estonia
2
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, UK
3
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, Yangzhou 225009, China
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Siteler Mahallesi, 1307 Sokak, Ahmet Kartal Konutlari, A-1 Blok, No:7/2, Konyaalti, 07070 Antalya, Turkey
*
Author to whom correspondence should be addressed.
Symmetry 2020, 12(1), 68; https://doi.org/10.3390/sym12010068
Received: 14 December 2019 / Revised: 23 December 2019 / Accepted: 26 December 2019 / Published: 1 January 2020
(This article belongs to the Special Issue Noether’s Symmetry Approach in Gravity and Cosmology)
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. View Full-Text
Keywords: Noether symmetry; exact solutions; spherical symmetry; Gauss-Bonnet Noether symmetry; exact solutions; spherical symmetry; Gauss-Bonnet
MDPI and ACS Style

Bahamonde, S.; Dialektopoulos, K.; Camci, U. Exact Spherically Symmetric Solutions in Modified Gauss–Bonnet Gravity from Noether Symmetry Approach. Symmetry 2020, 12, 68.

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