Hamiltonian Dynamics of a spaceship in Alcubierre and Gödel metrics: Recursion operators and underlying master symmetries

Hounkonnou, Mahouton Norbert; Justin, Landalidji, Mahougnon; Mitrovíc, Melanija

doi:10.48550/arxiv.2201.00380

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2022

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“…This is reminiscent to the well known Oevel formulas (see [31,13,37,38,19,20]). Finally, it is worth mentioning a generalization of the α-Poisson brackets (29) as follows:…”

Section: Family Of Conserved Quantitiesmentioning

confidence: 67%

Einstein field equation, recursion operators, Noether and master symmetries in conformable Poisson manifolds

Hounkonnou¹,

Justin²,

Mitrovic³

2022

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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-Lemaître-Robertson-Walker (FLRW) manifolds, and derive 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.

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“…This is reminiscent to the well known Oevel formulas (see [31,13,37,38,19,20]). Finally, it is worth mentioning a generalization of the α-Poisson brackets (29) as follows:…”

Section: Family Of Conserved Quantitiesmentioning

confidence: 67%