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.

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.

SYMMETRY AND CONSERVATION LAW CLASSIFICATION AND EXACT SOLUTIONS TO THE GENERALIZED KdV TYPES OF EQUATIONS

2012 ◽  
Vol 22 (08) ◽  
pp. 1250188 ◽  
Author(s):  
HANZE LIU ◽  
JIBIN LI ◽  
LEI LIU
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Conservation Law ◽  
Vector Fields ◽  
Nonlinear Partial Differential Equations ◽  
Second Order ◽  
Analytic Method ◽  
Composite Function ◽  
Symmetry And Conservation Law

In this paper, complete geometric symmetry and conservation law classification of the generalized KdV types of equations are investigated. All of the geometric vector fields and second-order multipliers for the equations are obtained, and the corresponding conservation laws of the equations are presented explicitly. These comprise all of the second-order conservation laws for the equations. Furthermore, an analytic method is developed for dealing with the exact solutions to the generalized nonlinear partial differential equations with composite function terms.

scholarly journals Symmetries, pseudosymmetries and conservation laws in Lagrangian and Hamiltonian k-symplectic formalisms

2016 ◽  
Vol 13 (03) ◽  
pp. 1650026
Author(s):  
Florian Munteanu
Keyword(s):  
Conservation Laws ◽  
Hamiltonian Systems ◽  
Conservation Law ◽  
Type Theorem ◽  
Natural Extension ◽  
Lagrangian Systems ◽  
Symmetry And Conservation Law

In this paper, we will present Lagrangian and Hamiltonian [Formula: see text]-symplectic formalisms, we will recall the notions of symmetry and conservation law and we will define the notion of pseudosymmetry as a natural extension of symmetry. Using symmetries and pseudosymmetries, without the help of a Noether type theorem, we will obtain new kinds of conservation laws for [Formula: see text]-symplectic Hamiltonian systems and [Formula: see text]-symplectic Lagrangian systems.

The direction of time and the equivalence of ‘expanding’ and ‘contracting’ world-models

1964 ◽  
Vol 60 (3) ◽  
pp. 575-579 ◽  
Author(s):  
D. L. Schumacher
Keyword(s):  
Conservation Laws ◽  
Explicit Form ◽  
Quantum Measurement ◽  
Conservation Law ◽  
Line Element ◽  
Cosmic Time ◽  
De Sitter Space ◽  
De Sitter ◽  
Global Coherence ◽  
Elliptic Model

AbstractIt is assumed initially that only the increase of entropy defines locally the sense of advance of time. This assumption, together with the feature of global coherence of statistical processes, which is provided by the cosmic line-element, imply that there is a unique way of associating the standards with the cosmic statistical processes. There is hence a connexion between the sense of divergence of geodesics of fundamental observers and the cosmic time-sense. This is in keeping with the unmodified conservation laws of gravitation and the analogous adiabatic conservation law quite generally without dependence on the explicit form of the line element. These remarks correspond exactly to consequences of the ‘elliptic’ model in the case of de Sitter space, obtained by entirely separate geometrical considerations. A remark is made with regard to the irreversibility associated with quantum measurement.

scholarly journals Conservation laws of coupled semilinear wave equations

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640004 ◽  
Author(s):  
Stephen C. Anco ◽  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Wave Equations ◽  
Gordon Equation ◽  
Complete Classification ◽  
Conserved Quantities ◽  
Semilinear Wave Equations ◽  
Two Component ◽  
Klein Gordon ◽  
Klein Gordon Equation

A complete classification of all low-order conservation laws is carried out for a system of coupled semilinear wave equations which is a natural two-component generalization of the nonlinear Klein–Gordon equation. The conserved quantities defined by these conservation laws are derived and their physical meaning is discussed.

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+.

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