A conjecture about the general cosmological solution of Einstein's equations

TL;DR

This paper proposes a new idea that the synchronization of oscillations in spacetime near singularities, modeled after Kuramoto oscillators, could simplify understanding the complex solutions of Einstein's equations in cosmology.

Contribution

It introduces the concept that spacetime Mixmaster oscillations may synchronize near singularities, offering a novel approach to analyzing inhomogeneous cosmological solutions.

Findings

Synchronization of oscillations could occur near singularities.

Kuramoto model analogy provides a new perspective.

Potential simplification of Einstein's equations solutions.

Abstract

We introduce consideration of a new factor, synchronisation of spacetime Mixmaster oscillations, that may play a simplifying role in understanding the nature of the general inhomogeneous cosmological solution to Einstein's equations. We conjecture that, on approach to a singularity, the interaction of spacetime Mixmaster oscillations in different regions of an inhomogeneous universe can produce a synchronisation of these oscillations through a coupling to their mean field in the way first demonstrated by the Kuramoto coupled oscillator model.