Isochronous solutions of Einstein's equations and their Newtonian limit

TL;DR

This paper reviews isochronous solutions in Einstein's equations, demonstrating their Newtonian limit aligns with non-relativistic dynamics, thus bridging relativistic and classical cosmological models.

Contribution

It introduces the concept of isochronous solutions in general relativity and analyzes their Newtonian limit, extending previous non-relativistic results to relativistic cosmology.

Findings

Isochronous solutions exist in Einstein's equations.

The Newtonian limit of these solutions matches non-relativistic results.

The work bridges relativistic and classical descriptions of cosmology.

Abstract

It has been recently demonstrated that it is possible to construct isochronous cosmologies, extending to general relativity a result valid for non-relativistic Hamiltonian systems. In this paper we review these findings and we discuss the Newtonian limit of these isochronous spacetimes, showing that it reproduces the analogous findings in the context of non-relativistic dynamics.