Einstein Field Equation, Recursion Operators, Noether and Master Symmetries in Conformable Poisson Manifolds

被引：1

作者：

Hounkonnou, Mahouton Norbert ^{[1
,2
]}

Landalidji, Mahougnon Justin ^{[1
,2
]}

Mitrovic, Melanija ^{[1
,2
,3
]}

机构：

[1] Univ Abomey Calavi, Int Chair Math Phys & Applicat ICMPA UNESCO Chair, 072 BP 50, Cotonou, Benin

[2] Int Ctr Res & Adv Studies Math & Comp Sci & Appli, 072 BP 50, Cotonou, Benin

[3] Univ Nis, Fac Mech Engn CAM FMEN, Ctr Appl Math, A Medvedeva 14, Nish 18000, Serbia

来源：

UNIVERSE | 2022年 / 8卷 / 04期

关键词：

Einstein field equation; recursion operator; Noether symmetry; master symmetry; conformable differential; Poisson manifold; SUPERINTEGRABILITY; INTEGRALS; DYNAMICS; SYSTEM;

D O I：

10.3390/universe8040247

中图分类号：

P1 [天文学];

学科分类号：

0704 ;

摘要：

We show that a Minkowski phase space endowed with a bracket relatively to a conformable differential realizes a Poisson algebra, confering a bi-Hamiltonian structure to the resulting manifold. We infer that the related Hamiltonian vector field is an infinitesimal Noether symmetry, and compute the corresponding deformed recursion operator. Besides, using the Hamiltonian-Jacobi separability, we construct recursion operators for Hamiltonian vector fields in conformable Poisson-Schwarzschild and Friedmann-Lemaitre-Robertson-Walker (FLRW) manifolds, and derive the related constants of motion, Christoffel symbols, components of Riemann and Ricci tensors, Ricci constant and components of Einstein tensor. We highlight the existence of a hierarchy of bi-Hamiltonian structures in both the manifolds, and compute a family of recursion operators and master symmetries generating the constants of motion.

引用

页数：27