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.

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 Renormalizability of Alternative Theories of Gravity: Differences between Power Counting and Entropy Argument

Universe ◽  
2021 ◽  
Vol 7 (5) ◽  
pp. 148
Author(s):  
Francesco Bajardi ◽  
Francesco Bascone ◽  
Salvatore Capozziello
Keyword(s):  
General Relativity ◽  
Teleparallel Gravity ◽  
Power Counting ◽  
Alternative Theories Of Gravity ◽  
Spherically Symmetric ◽  
Asymptotic Safety ◽  
Renormalizable Theory ◽  
Theories Of Gravity ◽  
Working Out ◽  
Alternative Theories

It is well known that General Relativity cannot be considered under the standard of a perturbatively renormalizable quantum field theory, but asymptotic safety is taken into account as a possibility for the formulation of gravity as a non-perturbative renormalizable theory. Recently, the entropy argument has however stepped into the discussion claiming for a “no-go” to the asymptotic safety argument. In this paper, we present simple counter-examples, considering alternative theories of gravity, to the entropy argument as further indications, among others, on the possible flows in the assumptions on which the latter is based. We considered different theories, namely curvature-based extensions of General Relativity as f(R), f(G), extensions of teleparallel gravity as f(T), and Horava–Lifshitz gravity, working out the explicit spherically symmetric solutions in order to make a comparison between power counting and the entropy argument. Even in these cases, inconsistencies were found.

scholarly journals Static spherically symmetric solutions in a subclass of Horndeski theories of gravity

2018 ◽  
Vol 15 (09) ◽  
pp. 1850152 ◽  
Author(s):  
Lorenzo Sebastiani
Keyword(s):  
General Relativity ◽  
Black Hole ◽  
Integration Constant ◽  
Spherically Symmetric ◽  
Rotation Curves ◽  
Spherically Symmetric Solutions ◽  
Euclidean Action ◽  
Theories Of Gravity ◽  
Static Spherically Symmetric Solutions

In this paper, we will consider a subclass of models of Horndeski theories of gravity and we will check for several Static Spherically Symmetric solutions. We will find a model which admits an exact black hole (BH) solution and we will study its thermodynamics by using the Euclidean Action. We will see that, in analogy with the case of General Relativity (GR), the integration constant of the solution can be identified with the mass of the BH itself. Other solutions will be discussed, by posing special attention on the possibility of reproducing the observed profiles of the rotation curves of galaxies. a

scholarly journals Perturbations of Keplerian orbits in stationary spherically symmetric spacetimes

2014 ◽  
Vol 23 (05) ◽  
pp. 1450049 ◽  
Author(s):  
Matteo Luca Ruggiero
Keyword(s):  
Power Laws ◽  
Approximation Order ◽  
Alternative Theories Of Gravity ◽  
Spherically Symmetric ◽  
Central Mass ◽  
Secular Variations ◽  
Analytic Expressions ◽  
Theories Of Gravity ◽  
The Impact ◽  
Alternative Theories

We study spherically symmetric perturbations determined by alternative theories of gravity to the gravitational field of a central mass in General Relativity (GR). In particular, we focus on perturbations in the form of power laws and calculate their effect on the secular variations of the orbital elements of a Keplerian orbit. We show that, to lowest approximation order, only the argument of pericenter and mean anomaly undergo secular variations; furthermore, we calculate the variation of the orbital period. We give analytic expressions for these variations which can be used to constrain the impact of alternative theories of gravity.

scholarly journals Embedding Black Holes and Other Inhomogeneities in the Universe in Various Theories of Gravity: A Short Review

Universe ◽  
2018 ◽  
Vol 4 (10) ◽  
pp. 109 ◽  
Author(s):  
Valerio Faraoni
Keyword(s):  
Black Holes ◽  
Short Review ◽  
Alternative Theories Of Gravity ◽  
Spherically Symmetric ◽  
Event Horizons ◽  
Interesting Class ◽  
Theories Of Gravity ◽  
The Universe ◽  
Alternative Theories ◽  
Trapping Horizons

Classic black hole mechanics and thermodynamics are formulated for stationary black holes with event horizons. Alternative theories of gravity of interest for cosmology contain a built-in time-dependent cosmological “constant” and black holes are not stationary. Realistic black holes are anyway dynamical because they interact with astrophysical environments or, at a more fundamental level, because of backreaction by Hawking radiation. In these situations, the teleological concept of event horizon fails and apparent or trapping horizons are used instead. Even as toy models, black holes embedded in cosmological “backgrounds” and other inhomogeneous universes constitute an interesting class of solutions of various theories of gravity. We discuss the known phenomenology of apparent and trapping horizons in these geometries, focusing on spherically symmetric inhomogeneous universes.

Sign in / Sign up

Export Citation Format

Share Document