scholarly journals New spherically symmetric solutions in f (R)-gravity by Noether symmetries

2012 ◽  
Vol 44 (8) ◽  
pp. 1881-1891 ◽  
Author(s):  
Salvatore Capozziello ◽  
Noemi Frusciante ◽  
Daniele Vernieri
Keyword(s):  
Spherically Symmetric ◽  
Noether Symmetries ◽  
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 Higher Dimensional Static and Spherically Symmetric Solutions in Extended Gauss–Bonnet Gravity

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 372 ◽  
Author(s):  
Francesco Bajardi ◽  
Konstantinos F. Dialektopoulos ◽  
Salvatore Capozziello
Keyword(s):  
Topological Invariant ◽  
Spherically Symmetric ◽  
Noether Symmetries ◽  
Curvature Scalar ◽  
Bonnet Gravity ◽  
Higher Dimensional ◽  
Point Transformations ◽  
Spherically Symmetric Solutions ◽  
Functional Forms ◽  
Symmetric Spacetime

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.

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.

Classification of Static Spherically Symmetric Spacetimes by Noether Symmetries

2013 ◽  
Vol 52 (10) ◽  
pp. 3534-3542 ◽  
Author(s):  
Ashfaque H. Bokhari ◽  
A. G. Johnpillai ◽  
A. H. Kara ◽  
F. M. Mahomed ◽  
F. D. Zaman
Keyword(s):  
Spherically Symmetric ◽  
Noether Symmetries ◽  
Symmetric Spacetimes ◽  
Spherically Symmetric Spacetimes ◽  
Static Spherically Symmetric Spacetimes

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.

scholarly journals Intersecting Electric and Magnetic p-branes: Spherically Symmetric Solutions

1999 ◽  
Vol 31 (11) ◽  
pp. 1681-1702 ◽  
Author(s):  
K. A. Bronnikov ◽  
U. Kasper ◽  
M. Rainer
Keyword(s):  
Spherically Symmetric ◽  
Spherically Symmetric Solutions
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