Isochronous Spacetimes

TL;DR

This paper explores extending the concept of isochronous (periodic) many-body systems from nonrelativistic physics to general relativity, with potential implications for cosmology.

Contribution

It reviews and advances the idea of creating isochronous spacetimes within general relativity, broadening the scope of previous nonrelativistic models.

Findings

Demonstrated the feasibility of isochronous spacetime models in a relativistic context.

Showed that these models can approximate or replicate complex gravitational systems.

Explored potential applications to cosmological scenarios.

Abstract

The possibility has been recently demonstrated to manufacture (nonrelativistic, Hamiltonian) many-body problems which feature an isochronous time evolution with an arbitrarily assigned period $T$ yet mimic with good approximation, or even exactly, any given many-body problem (within a quite large class, encompassing most of nonrelativistic physics) over times $\tilde{T}$ which may also be arbitrarily large (but of course such that $\tilde{T}<T$). In this paper we review and further explore the possibility to extend this finding to a general relativity context, so that it becomes relevant for cosmology.