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 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 Noether symmetries as a geometric criterion to select theories of gravity

2018 ◽  
Vol 15 (supp01) ◽  
pp. 1840007 ◽  
Author(s):  
Konstantinos F. Dialektopoulos ◽  
Salvatore Capozziello
Keyword(s):  
Exact Solutions ◽  
Cosmological Models ◽  
Noether Symmetry ◽  
Noether Symmetries ◽  
Field Equations ◽  
Geometric Criterion ◽  
Symmetry Approach ◽  
Theories Of Gravity ◽  
Gravity Theories

We review the Noether Symmetry Approach as a geometric criterion to select theories of gravity. Specifically, we deal with Noether Symmetries to solve the field equations of given gravity theories. The method allows to find out exact solutions, but also to constrain arbitrary functions in the action. Specific cosmological models are taken into account.

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 Nonstatic Spherically Symmetric Solutions for a Perfect Fluid in General Relativity

1976 ◽  
Vol 29 (2) ◽  
pp. 113 ◽  
Author(s):  
N Chakravarty ◽  
SB Dutta Choudhury ◽  
A Banerjee
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Dynamical Behaviour ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Spherically Symmetric Solutions ◽  
Spherically Symmetric Distribution ◽  
General Method

A general method is described by which exact solutions of Einstein's field equations are obtained for a nonstatic spherically symmetric distribution of a perfect fluid. In addition to the previously known solutions which are systematically derived, a new set of exact solutions is found, and the dynamical behaviour of the corresponding models is briefly discussed.

scholarly journals New Black Holes Solutions in a Modified Gravity

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
M. Hamani Daouda ◽  
Manuel E. Rodrigues ◽  
M. J. S. Houndjo
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Modified Gravity ◽  
Gauge Theories ◽  
Matter Content ◽  
Spherically Symmetric ◽  
Commutator Algebra ◽  
Spherically Symmetric Solutions ◽  
Basic Concepts ◽  
Rindler Acceleration

We present some basic concepts of a theory of modified gravity, inspired by the gauge theories, where the commutator algebra of covariant derivative gives us an added term with respect to the General Relativity, which represents the interaction of gravity with a substratum. New spherically symmetric solutions of this theory are obtained and can be viewed as solutions that reproduce the mass, the charge, the cosmological constant, and the Rindler acceleration, without coupling with the matter content, that is, in the vacuum.

scholarly journals F(R,G) Cosmology through Noether Symmetry Approach

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 719 ◽  
Author(s):  
Ugur Camci
Keyword(s):  
Cosmological Solution ◽  
First Integrals ◽  
Boundary Term ◽  
Noether Symmetry ◽  
Noether Symmetries ◽  
Real Numbers ◽  
Cosmological Scale ◽  
Symmetry Approach ◽  
Scale Factors ◽  
Functional Boundary

The F ( R , G ) theory of gravity, where R is the Ricci scalar and G is the Gauss-Bonnet invariant, is studied in the context of existence the Noether symmetries. The Noether symmetries of the point-like Lagrangian of F ( R , G ) gravity for the spatially flat Friedmann-Lemaitre-Robertson-Walker cosmological model is investigated. With the help of several explicit forms of the F ( R , G ) function it is shown how the construction of a cosmological solution is carried out via the classical Noether symmetry approach that includes a functional boundary term. After choosing the form of the F ( R , G ) function such as the case ( i ) : F ( R , G ) = f 0 R n + g 0 G m and the case ( i i ) : F ( R , G ) = f 0 R n G m , where n and m are real numbers, we explicitly compute the Noether symmetries in the vacuum and the non-vacuum cases if symmetries exist. The first integrals for the obtained Noether symmetries allow to find out exact solutions for the cosmological scale factor in the cases (i) and (ii). We find several new specific cosmological scale factors in the presence of the first integrals. It is shown that the existence of the Noether symmetries with a functional boundary term is a criterion to select some suitable forms of F ( R , G ) . In the non-vacuum case, we also obtain some extra Noether symmetries admitting the equation of state parameters w ≡ p / ρ such as w = − 1 , − 2 / 3 , 0 , 1 etc.

scholarly journals CONSISTENCY CONDITION OF SPHERICALLY SYMMETRIC SOLUTIONS IN f(R) GRAVITY

2009 ◽  
Vol 24 (04) ◽  
pp. 305-309 ◽  
Author(s):  
REZA SAFFARI ◽  
SOHRAB RAHVAR
Keyword(s):  
Modified Gravity ◽  
Symmetric Solution ◽  
Consistency Condition ◽  
Spherically Symmetric ◽  
Extra Condition ◽  
Spherically Symmetric Solutions ◽  
Gravity Equations

In this work we study the spherical symmetric solutions of f(R) gravity in the metric formalism. We show that for a generic f(R) gravity, the spherical symmetric solution is consistent with the modified gravity equations except in the case of imposing an extra condition for the metric.

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