Classification of a modified de Sitter metric by variational symmetries and conservation laws

2017 ◽  
Vol 14 (12) ◽  
pp. 1750182
Author(s):  
A. Beesham ◽  
B. B. I. Gadjagboui ◽  
A. H. Kara
Keyword(s):  
Conservation Laws ◽  
Noether Symmetries ◽  
De Sitter ◽  
Killing Vectors ◽  
Variational Symmetries ◽  
De Sitter Metric

Variational symmetries and conservation laws of a modified de Sitter metric are classified. The resulting Noether symmetries in each case are compared with conservation laws given by Killing vectors.

On the symmetry and conservation law classification of the de Sitter–Schwarzschild metric and the corresponding wave and Klein–Gordon equations

2020 ◽  
Vol 17 (11) ◽  
pp. 2050172
Author(s):  
Ashfaque H. Bokhari ◽  
A. H. Kara ◽  
F. D. Zaman ◽  
B. B. I. Gadjagboui
Keyword(s):  
Conservation Laws ◽  
Conservation Law ◽  
De Sitter ◽  
Killing Vectors ◽  
Schwarzschild Geometry ◽  
Klein Gordon ◽  
Spacetime Metric ◽  
Variational Symmetries ◽  
Symmetry And Conservation Law

The main purpose of this work is to focus on a discussion of Lie symmetries admitted by de Sitter–Schwarzschild spacetime metric, and the corresponding wave or Klein–Gordon equations constructed in the de Sitter–Schwarzschild geometry. The obtained symmetries are classified and the variational (Noether) conservation laws associated with these symmetries via the natural Lagrangians are obtained. In the case of the metric, we obtain additional variational ones when compared with the Killing vectors leading to additional conservation laws and for the wave and Klein–Gordon equations, the variational symmetries involve less tedious calculations as far as invariance studies are concerned.

scholarly journals Integrability of Riemann-Type Hydrodynamical Systems and Dubrovin’s Integrability Classification of Perturbed KdV-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1077
Author(s):  
Yarema A. Prykarpatskyy
Keyword(s):  
Conservation Laws ◽  
Hamiltonian Structure ◽  
Necessary Condition ◽  
Type Representation ◽  
Infinite Hierarchy ◽  
Polynomial Coefficients ◽  
Kdv Type Equations ◽  
Special Case

Dubrovin’s work on the classification of perturbed KdV-type equations is reanalyzed in detail via the gradient-holonomic integrability scheme, which was devised and developed jointly with Maxim Pavlov and collaborators some time ago. As a consequence of the reanalysis, one can show that Dubrovin’s criterion inherits important parts of the gradient-holonomic scheme properties, especially the necessary condition of suitably ordered reduction expansions with certain types of polynomial coefficients. In addition, we also analyze a special case of a new infinite hierarchy of Riemann-type hydrodynamical systems using a gradient-holonomic approach that was suggested jointly with M. Pavlov and collaborators. An infinite hierarchy of conservation laws, bi-Hamiltonian structure and the corresponding Lax-type representation are constructed for these systems.

scholarly journals Hamiltonian charges in the asymptotically de Sitter spacetimes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Maciej Kolanowski ◽  
Jerzy Lewandowski
Keyword(s):  
Phase Space ◽  
Initial Data ◽  
Exact Solutions ◽  
Gravitational Waves ◽  
Physical Meaning ◽  
De Sitter ◽  
Killing Vectors ◽  
Asymptotically Flat ◽  
Angular Momenta ◽  
The One

Abstract We generalize a notion of ‘conserved’ charges given by Wald and Zoupas to the asymptotically de Sitter spacetimes. Surprisingly, our construction is less ambiguous than the one encountered in the asymptotically flat context. An expansion around exact solutions possessing Killing vectors provides their physical meaning. In particular, we discuss a question of how to define energy and angular momenta of gravitational waves propagating on Kottler and Carter backgrounds. We show that obtained expressions have a correct limit as Λ → 0. We also comment on the relation between this approach and the one based on the canonical phase space of initial data at ℐ+.

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

On symmetries and conservation laws of some spacetimes in f(R, T) gravity

2019 ◽  
Vol 34 (36) ◽  
pp. 1975003
Author(s):  
Ashfaque H. Bokhari ◽  
A. H. Kara ◽  
B. Gadjagboui
Keyword(s):  
Conservation Laws ◽  
Detailed Analysis ◽  
Bianchi Type ◽  
Type I ◽  
Noether’S Theorem ◽  
Bianchi Type I ◽  
Plane Symmetric ◽  
Locally Rotationally Symmetric ◽  
Rotationally Symmetric ◽  
Variational Symmetries

We undertake a detailed analysis of the symmetry structures of the plane symmetric and the locally rotationally symmetric (LRS) Bianchi type I spacetimes in the [Formula: see text] gravity. In particular, we construct all the variational symmetries associated with its Lagrangian and, in some cases, construct the associated conservation laws using Noether’s theorem. Giving a comparison between isometries and variational symmetries, we give symmetry structures of some well-known spacetimes.

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