arXiv subjects
Publications and source records attributed to Farah Atieh.
Continuous generalizations of the Fibonacci sequence satisfy ODEs that are formal analogues of the Friedmann equation describing spatially homogeneous and isotropic cosmology in general relativity. These analogies are presented, together with their Lagrangian and Hamiltonian formulations and with an invariant of the Fibonacci sequence.
A formal analogy between the Friedmann equation of relativistic cosmology and models of convective-radiative cooling/heating of a body (including Newton's, Dulong-Petit's, Newton-Stefan's laws, and a generalization) is discussed. The analogy highlights Lagrangians, symmetries, and mathematical properties of the solutions of these cooling laws.
A Newtonian uniform ball expanding in empty space constitutes a common heuristic analogy for FLRW cosmology. We discuss possible implementations of the corresponding general-relativistic problem and a variety of new cosmological analogies arising from them. We highlight essential ingredients of the Newtonian analogy, including that the quasilocal energy is always `Newtonian' in the sense that the magnetic part of the Weyl tensor does not contribute to it. A symmetry of the Einstein-Friedmann equations produces another one in the original Newtonian system.