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

TL;DR

This paper explores the geometric and algebraic structures of conformable Poisson manifolds, revealing bi-Hamiltonian frameworks, recursion operators, and symmetries relevant to Einstein equations and cosmological models.

Contribution

It introduces new recursion operators and master symmetries in conformable Poisson manifolds, linking geometric structures to Einstein field equations and cosmological models.

Findings

Bi-Hamiltonian structures in conformable Poisson manifolds

Construction of recursion operators for Hamiltonian vector fields

Derivation of constants of motion and symmetries in cosmological models

Abstract

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-Lema\^itre-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.