scholarly journals Spherically symmetric solutions in f ( R ) gravity via the Noether symmetry approach

2007 ◽  
Vol 24 (8) ◽  
pp. 2153-2166 ◽  
Author(s):  
S Capozziello ◽  
A Stabile ◽  
A Troisi
Keyword(s):  
Noether Symmetry ◽  
Spherically Symmetric ◽  
Symmetry Approach ◽  
Spherically Symmetric Solutions

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

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 68 ◽  
Author(s):  
Sebastian Bahamonde ◽  
Konstantinos Dialektopoulos ◽  
Ugur Camci
Keyword(s):  
Vector Fields ◽  
Selection Criterion ◽  
Alternative Theories Of Gravity ◽  
Spherically Symmetric ◽  
Lie Point Symmetries ◽  
Noether Symmetries ◽  
Symmetry Approach ◽  
Point Transformations ◽  
Spherically Symmetric Solutions ◽  
Theories Of Gravity

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.

scholarly journals Exact Spherically Symmetric Solutions in Modified Teleparallel Gravity

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1462 ◽  
Author(s):  
Sebastian Bahamonde ◽  
Ugur Camci
Keyword(s):  
Exact Solutions ◽  
Modified Gravity ◽  
Teleparallel Gravity ◽  
Boundary Term ◽  
Spherically Symmetric ◽  
Noether Symmetries ◽  
Noether Theorem ◽  
Symmetry Approach ◽  
Spherically Symmetric Solutions ◽  
Teleparallel Theory

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.

scholarly journals Noether symmetry approach to the non-minimally coupled $$Y(R)F^2$$ gravity

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Özcan Sert ◽  
Fatma Çeliktaş
Keyword(s):  
Black Holes ◽  
Thermodynamic Properties ◽  
Noether Symmetry ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Lagrange Equations ◽  
Asymptotically Flat ◽  
Symmetry Approach ◽  
Static Solutions ◽  
Symmetry Assumption

Abstract We use Noether symmetry approach to find spherically symmetric static solutions of the non-minimally coupled electromagnetic fields to gravity. We construct the point-like Lagrangian under the spherical symmetry assumption. Then we determine Noether symmetry and the corresponding conserved charge. We derive Euler-Lagrange equations from this point-like Lagrangian and show that these equations are same with the differential equations derived from the field equations of the model. Also we give two new exact asymptotically flat solutions to these equations and investigate some thermodynamic properties of these black holes.

scholarly journals Teleparallel gravity with non-minimally coupled f-essence via Noether symmetry approach

2021 ◽  
Vol 1730 (1) ◽  
pp. 012022
Author(s):  
Kairat Myrzakulov ◽  
Duman Kenzhalin ◽  
Nurgissa Myrzakulov
Keyword(s):  
Teleparallel Gravity ◽  
Noether Symmetry ◽  
Symmetry Approach

scholarly journals FERMIONS IN THE BACKGROUND OF DILATONIC SPHALERONS

1994 ◽  
Vol 09 (40) ◽  
pp. 3731-3739 ◽  
Author(s):  
GEORGE LAVRELASHVILI
Keyword(s):  
Gauge Field ◽  
Field Potential ◽  
Spherically Symmetric ◽  
Yang Mills ◽  
Zero Modes ◽  
Discrete Sequence ◽  
Number Of Zeros ◽  
Spherically Symmetric Solutions ◽  
Static Spherically Symmetric Solutions

We discuss the properties and interpretation of a discrete sequence of a static spherically symmetric solutions of the Yang-Mills dilaton theory. This sequence is parametrized by the number of zeros, n, of a component of the gauge field potential. It is demonstrated that solutions with odd n possess all the properties of the sphaleron. It is shown that there are normalizable fermion zero modes in the background of these solutions. The question of instability is critically analyzed.

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