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Symmetry
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Noether’s Symmetry Approach in Gravity and Cosmology
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Noether’s Symmetry Approach in Gravity and Cosmology

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (31 July 2020) | Viewed by 10069

Special Issue Editors

Dr. Sebastián Bahamonde

E-Mail Website
Guest Editor
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
Interests: modified theories of gravity; cosmology; teleparallel gravity
Special Issues, Collections and Topics in MDPI journals
Prof. Mir Faizal

E-Mail Website
Guest Editor
1. Department of Physics and Astronomy, University of Lethbridge, 4401 University Drive, Lethbridge, AB T1K 3M4, Canada
2. Irving K. Barber School of Arts and Sciences, University of British Columbia, Okanagan, 3333 University Way, Kelowna, BC V1V 1V7, Canada
Interests: quantum gravity; string theory; high energy phenomenology

Special Issue Information

Dear Colleagues,

The Noether’s theorem is one of the most beautiful theorems in mathematics that allows us to find symmetries for a certain model, to then to use them to reduce its dynamical system and find exact solutions. This theorem has been widely used in gravity and cosmology to find exact solutions.

An enormous literature exists about modified theories of gravity, but these theories have (in general) complicated partial differential equations, and therefore, it is not so easy to find exact solutions for those models. To go beyond general relativity (GR) or the standard model of cosmology, it is important to investigue and find new exact solutions, to then compare them with the standard solutions known in GR. This might help to analyse the differences between modified theories and GR. The main aim of this Special Edition is to invite researchers from the subjects of gravity and cosmology to submit their work, in which one can use the Noether’s symmetry approach to find exact solutions.

Dr. Sebastián Bahamonde
Prof. Mir Faizal
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Noether symmetries
  • Noether’s theorem
  • Exact solutions
  • Gravity
  • Cosmology
  • Modified gravity
  • Conserved quantities
  • Symmetries
  • Astrophysics solutions

Published Papers (4 papers)

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Research

14 pages, 343 KiB  
Article
Cosmological Solutions for the Geometrical Scalar-Tensor with the Potential Determined by the Noether Symmetry Approach
by Adriano B. Barreto and Gilberto M. Kremer
Symmetry 2020, 12(7), 1110; https://doi.org/10.3390/sym12071110 - 3 Jul 2020
Cited by 1 | Viewed by 1600
Abstract
The aim of this work is to study a scalar-tensor theory where owing to Palatini’s variational method the space-time is endowed with a geometrical structure of Weyl integrable type. The geometrical nature of the scalar field is related to the non-metricity so that [...] Read more.
The aim of this work is to study a scalar-tensor theory where owing to Palatini’s variational method the space-time is endowed with a geometrical structure of Weyl integrable type. The geometrical nature of the scalar field is related to the non-metricity so that the theory is known as geometrical scalar-tensor. On the framework of Weyl transformations, a non-minimally coupled scalar-tensor theory on the Jordan frame corresponds to a minimally coupled Einstein–Hilbert action on the Einstein frame. The scalar potential is selected by the Noether symmetry approach in order to obtain conserved quantities for the FRW cosmological model. Exact solutions are obtained and analyzed in the context of the cosmological scenarios consistent with an expanding universe. A particular case is matched in each frame and the role of scalar field as a dark energy component is discussed. Full article
(This article belongs to the Special Issue Noether’s Symmetry Approach in Gravity and Cosmology)
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11 pages, 304 KiB  
Article
Higher Dimensional Static and Spherically Symmetric Solutions in Extended Gauss–Bonnet Gravity
by Francesco Bajardi, Konstantinos F. Dialektopoulos and Salvatore Capozziello
Symmetry 2020, 12(3), 372; https://doi.org/10.3390/sym12030372 - 2 Mar 2020
Cited by 38 | Viewed by 2606
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Noether’s Symmetry Approach in Gravity and Cosmology)
18 pages, 359 KiB  
Article
Exact Spherically Symmetric Solutions in Modified Gauss–Bonnet Gravity from Noether Symmetry Approach
by Sebastian Bahamonde, Konstantinos Dialektopoulos and Ugur Camci
Symmetry 2020, 12(1), 68; https://doi.org/10.3390/sym12010068 - 1 Jan 2020
Cited by 17 | Viewed by 2079
Abstract
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 [...] Read more.
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. Full article
(This article belongs to the Special Issue Noether’s Symmetry Approach in Gravity and Cosmology)
24 pages, 416 KiB  
Article
Exact Spherically Symmetric Solutions in Modified Teleparallel Gravity
by Sebastian Bahamonde and Ugur Camci
Symmetry 2019, 11(12), 1462; https://doi.org/10.3390/sym11121462 - 28 Nov 2019
Cited by 32 | Viewed by 3100
Abstract
Finding spherically symmetric exact solutions in modified gravity is usually a difficult task. In this paper, we use Noether symmetry approach for a modified teleparallel theory of gravity labeled as f ( T , B ) gravity where T is the scalar torsion [...] Read more.
Finding spherically symmetric exact solutions in modified gravity is usually a difficult task. In this paper, we use Noether symmetry approach for a modified teleparallel theory of gravity labeled as f ( T , B ) gravity where T is the scalar torsion and B the boundary term. Using Noether theorem, we were able to find exact spherically symmetric solutions for different forms of the function f ( T , B ) coming from Noether symmetries. Full article
(This article belongs to the Special Issue Noether’s Symmetry Approach in Gravity and Cosmology)
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