A cosmological study of Einstein–Skyrme model in anisotropic Kantowski–Sachs spacetime using Lie and Noether symmetries

2018 ◽  
Vol 15 (06) ◽  
pp. 1850089 ◽  
Author(s):  
Santu Mondal ◽  
Sourav Dutta ◽  
Manjusha Tarafdar ◽  
Subenoy Chakraborty
Keyword(s):  
Lie Algebra ◽  
Evolution Equations ◽  
Einstein Gravity ◽  
Lie Symmetry ◽  
Noether Symmetry ◽  
Noether Symmetries ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Unknown Parameters ◽  
Augmented Space

The present work deals with anisotropic (but zero heat flux) Skyrme fluid in a locally rotational Kantowski–Sachs (KS) spacetime in the background of Einstein gravity. The Lie point symmetry is imposed to the system of Einstein field equations and unknown parameters are either determined or interrelated by the imposition of the symmetry. Subsequently, Noether symmetry, a point-like symmetry of the Lagrangian is used and it is found that the Lie algebra of the Noether symmetry is a subalgebra of the corresponding Lie algebra of the Lie symmetry. Then a point transformation in the 2D augmented space is taken in such a manner that one of the variables becomes cyclic and hence the Lagrangian as well as the evolution equations are simplified to a great extent. Finally, solutions to the physical system are presented and are analyzed physically.

scholarly journals The Physical Significance of Time Conformal Minkowski Spacetime

2020 ◽  
Vol 39 (2) ◽  
pp. 365-370
Author(s):  
Farhad Ali ◽  
Muhammad Asif Jan ◽  
Wali Khan Mashwani ◽  
Rashida Adeeb Khanum ◽  
Hidayat Ullah Khan
Keyword(s):  
Cosmological Constant ◽  
Energy Content ◽  
Einstein Field Equation ◽  
Minkowski Spacetime ◽  
Conformal Factor ◽  
Noether Symmetry ◽  
Noether Symmetries ◽  
Einstein Field Equations ◽  
Field Equations ◽  
General Time

The Minkowsiki spacetime is flat and there is no source of gravitation. The time conformal factor is adding some cuvature to this spacetime which introduces some source of gravitation to the spacetime. For the Minkowski spacetime the Einstein Field equation tells nothing, because all the components of the Ricci curvature tensor are zero, but for the time conformal Minkowski spacetime some of them are non zero. Calculating the components of the Ricci tensor and using the Einstein field equations, expressions for the cosmological constant are cacultaed. These expressions give some information for the cosmological constant. Generally, the Noether symmetry generator corresponding to the energy content in the spacetime disapeares by introducing the time conformal factor, but our investigations in this paper reveals that it appears somewhere with some re-scale factor. The appearance of the time like isometry along with some re-scaling factor will rescale the energy content in the corresponding particular time conformal Minkowski spacetime. A time conformal factor of the form () is introduced in the Minkowski spacetime for the invistigation of the cosmological constant. The Noether symmetry equation is used for the Lagrangian of general time conformal Minkowski spacetime to find all those particular Minkowski spacetimes that admit the time conformal factor. Besides the Noether symmetries the cosmology constant is calculated in the corresponding spacetimes.

scholarly journals SPIN-1 GRAVITATIONAL WAVES: THEORETICAL AND EXPERIMENTAL ASPECTS

2006 ◽  
Vol 03 (03) ◽  
pp. 451-469 ◽  
Author(s):  
F. CANFORA ◽  
L. PARISI ◽  
G. VILASI
Keyword(s):  
Physical Properties ◽  
Exact Solutions ◽  
Gravitational Waves ◽  
Lie Algebra ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Gravitational Fields ◽  
Killing Fields

Exact solutions of Einstein field equations invariant for a non-Abelian bidimensional Lie algebra of Killing fields are described. Physical properties of these gravitational fields are studied, their wave character is checked by making use of covariant criteria and the observable effects of such waves are outlined. The possibility of detection of these waves with modern detectors, spherical resonant antennas in particular, is sketched.

scholarly journals Lifts of Symmetric Tensors: Fluids, Plasma, and Grad Hierarchy

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 907 ◽  
Author(s):  
Oğul Esen ◽  
Miroslav Grmela ◽  
Hasan Gümral ◽  
Michal Pavelka
Keyword(s):  
Kinetic Theory ◽  
Lie Algebra ◽  
Particle Motion ◽  
Evolution Equations ◽  
Poisson Brackets ◽  
Hamiltonian Approach ◽  
Symmetric Tensors ◽  
Field Equations ◽  
Algebra Homomorphisms

Geometrical and algebraic aspects of the Hamiltonian realizations of the Euler’s fluid and the Vlasov’s plasma are investigated. A purely geometric pathway (involving complete lifts and vertical representatives) is proposed, which establishes a link from particle motion to evolution of the field variables. This pathway is free from Poisson brackets and Hamiltonian functionals. Momentum realizations (sections on T * T * Q ) of (both compressible and incompressible) Euler’s fluid and Vlasov’s plasma are derived. Poisson mappings relating the momentum realizations with the usual field equations are constructed as duals of injective Lie algebra homomorphisms. The geometric pathway is then used to construct the evolution equations for 10-moments kinetic theory. This way the entire Grad hierarchy (including entropic fields) can be constructed in a purely geometric way. This geometric way is an alternative to the usual Hamiltonian approach to mechanics based on Poisson brackets.

A study of dynamical equations for non-minimally coupled scalar field using Noether symmetric approach

2016 ◽  
Vol 31 (19) ◽  
pp. 1650116 ◽  
Author(s):  
Sourav Dutta ◽  
Madan Mohan Panja ◽  
Subenoy Chakraborty
Keyword(s):  
Scalar Field ◽  
Infinitesimal Generator ◽  
Einstein Gravity ◽  
Matter Content ◽  
The Self ◽  
Noether Symmetry ◽  
Dynamical Equations ◽  
Augmented Space ◽  
Constants Of Motion ◽  
Scalar Field Cosmology

Non-minimally coupled scalar field cosmology has been studied in this work within the framework of Einstein gravity. In the background of homogeneous and isotropic Friedmann–Lemaitre–Robertson–Walker (FLRW) spacetime non-minimally coupled scalar field having self-interacting potential is taken as the source of the matter content. The constraint of imposing Noether symmetry on the Lagrangian of the system not only determines the infinitesimal generator (the symmetry vector) but also the coupling function and the self-interacting potential for the scalar field. By choosing appropriately a point transformation in the augmented space, one of the transformed variables is cyclic for the Lagrangian. Finally, using constants of motion, the solutions are analyzed.

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 Noether symmetries and duality transformations in cosmology

2016 ◽  
Vol 31 (32) ◽  
pp. 1650183 ◽  
Author(s):  
Andronikos Paliathanasis ◽  
Salvatore Capozziello
Keyword(s):  
Discrete Symmetry ◽  
Scale Factor ◽  
Noether Symmetry ◽  
Linear Potential ◽  
Noether Symmetries ◽  
Field Equations ◽  
Duality Transformation ◽  
Normal Coordinates ◽  
Duality Transformations ◽  
Duality Symmetry

We discuss the relation between Noether (point) symmetries and discrete symmetries for a class of minisuperspace cosmological models. We show that when a Noether symmetry exists for the gravitational Lagrangian, then there exists a coordinate system in which a reversal symmetry exists. Moreover, as far as concerns, the scale-factor duality symmetry of the dilaton field, we show that it is related to the existence of a Noether symmetry for the field equations, and the reversal symmetry in the normal coordinates of the symmetry vector becomes scale-factor duality symmetry in the original coordinates. In particular, the same point symmetry as also the same reversal symmetry exists for the Brans–Dicke scalar field with linear potential while now the discrete symmetry in the original coordinates of the system depends on the Brans–Dicke parameter and it is a scale-factor duality when [Formula: see text]. Furthermore, in the context of the O’Hanlon theory for f(R)-gravity, it is possible to show how a duality transformation in the minisuperspace can be used to relate different gravitational models.

scholarly journals Quintom cosmological model and some possible solutions using Lie and Noether symmetries

2016 ◽  
Vol 25 (14) ◽  
pp. 1650110 ◽  
Author(s):  
Sourav Dutta ◽  
Muthusamy Lakshmanan ◽  
Subenoy Chakraborty
Keyword(s):  
Lie Algebra ◽  
Physical System ◽  
Three Dimensional ◽  
Noether Symmetry ◽  
Conserved Quantities ◽  
Considerable Simplification ◽  
Present Context ◽  
Augmented Space ◽  
Constants Of Motion ◽  
Flrw Universe

The present work deals with a quintom model of dark energy in the framework of a spatially flat isotropic and homogeneous Friedmann–Lemaitre–Robertson–Walker (FLRW) universe. At first, Lie point symmetry is imposed to the system and the unknown coupled potential of the model is determined. Then Noether symmetry, which is also a point like symmetry of the Lagrangian, is imposed on the physical system and the potential takes a general form. It is shown that the Lie algebra of Noether symmetry is a sub-algebra of the corresponding Lie algebra of the Lie symmetry. Finally, a point transformation in the three-dimensional augmented space is performed suitably so that one of the variables become cyclic and as a result there is considerable simplification to the physical system. Hence, conserved quantities (i.e. constants of motion) are expressed in a compact form and cosmological solutions are evaluated and analyzed in the present context.

Lie and Noether symmetry analysis in Brans–Dicke cosmology

2018 ◽  
Vol 33 (34) ◽  
pp. 1850198 ◽  
Author(s):  
Sourav Dutta ◽  
Santu Mondal
Keyword(s):  
Evolution Equations ◽  
Analytic Solution ◽  
State Parameter ◽  
Lie Symmetry ◽  
Noether Symmetry ◽  
Coordinate Systems ◽  
Group Invariant ◽  
Augmented System ◽  
Equation Of State Parameter ◽  
Group Invariant Solutions

This paper is aimed to study the group invariant solutions of the evolution equations in Brans–Dicke cosmology. In this context, we have considered the flat homogeneous Brans–Dicke (BD) scalar field in the background of flat homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker (FLRW) cosmological model and have used Lie and Noether symmetry on the augmented system. From Lie symmetry we have determined the unknown potential for two different values of the equation of state parameter w. Then assuming that the Lagrangian admits a Noether symmetry, an analytic solution of the system is obtained in both old and new coordinate systems.

Classical and quantum cosmology in f(T)-gravity theory: A Noether symmetry approach

2021 ◽  
Author(s):  
Roshni Bhaumik ◽  
Sourav Dutta ◽  
Subenoy Chakraborty
Keyword(s):  
Quantum Cosmology ◽  
Functional Form ◽  
Gravity Theory ◽  
Noether Symmetry ◽  
Field Equations ◽  
Time Model ◽  
Symmetry Approach ◽  
Walker Metric ◽  
Augmented Space ◽  
Space Time Model

In the framework of [Formula: see text]-gravity theory, classical and quantum cosmology has been studied in this work for Friedmann Lemaitre Robertson Walker Metric (FLRW) space-time model. The Noether symmetry, a point-like symmetry of the Lagrangian, is used to the physical system and a specific functional form of [Formula: see text] is determined. A point transformation in the 2D augmented space restricts one of the variables to be cyclic so that the Lagrangian as well as the field equations are simplified so that they are solvable. Lastly, for quantum cosmology, the WD equation is constructed and a possible solution has been evaluated.

scholarly journals A study of phantom scalar field cosmology using Lie and Noether symmetries

2016 ◽  
Vol 25 (05) ◽  
pp. 1650051 ◽  
Author(s):  
Sourav Dutta ◽  
Subenoy Chakraborty
Keyword(s):  
Scalar Field ◽  
State Parameter ◽  
Einstein Gravity ◽  
Matter Field ◽  
Lie Symmetry ◽  
Kinetic Term ◽  
Noether Symmetries ◽  
Phantom Scalar ◽  
Scalar Field Cosmology ◽  
Phantom Scalar Field

The paper deals with phantom scalar field cosmology in Einstein gravity. At first, using Lie symmetry, the coupling function to the kinetic term and the potential function of the scalar field and the equation of state parameter of the matter field are determined and a simple solution is obtained. Subsequently, Noether symmetry is imposed on the Lagrangian of the system. The symmetry vector is obtained and the potential takes a very general form from which potential using Lie symmetry can be obtained as a particular case. Then, we choose a point transformation [Formula: see text] such that one of the transformed variables (say [Formula: see text]) is a cyclic for the Lagrangian. Using conserved charge (corresponding to the cyclic coordinate) and the constant of motion, solutions are obtained.

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