Hamiltonian Dynamics of a spaceship in Alcubierre and G\"odel metrics: Recursion operators and underlying master symmetries

TL;DR

This paper investigates the Hamiltonian dynamics of a spaceship within Alcubierre and G"odel spacetime metrics, focusing on recursion operators and master symmetries to understand conserved quantities and system behavior.

Contribution

It introduces the derivation of Hamiltonian vector fields, constructs recursion operators, and characterizes master symmetries specific to these spacetime backgrounds.

Findings

Identification of Hamiltonian vector fields for the systems

Construction of recursion operators generating constants of motion

Characterization of relevant master symmetries

Abstract

We study the Hamiltonian dynamics of a spaceship in the background of Alcubierre and G\"odel metrics. We derive the Hamiltonian vector fields governing the system evolution, construct and discuss related recursion operators generating the constants of motion. Besides, we characterize relevant master symmetries.