Gravity and Complexity

TL;DR

This paper explores the complex and potentially undecidable dynamics of solutions to Einstein's equations, suggesting they may exhibit unpredictability surpassing traditional chaos, akin to Turing machine computation.

Contribution

It provides a heuristic analysis indicating that cosmological models governed by Einstein's equations can have undecidable and highly unpredictable behaviors.

Findings

Systems may have undecidable features.

Predictability can be fundamentally limited.

Dynamics could surpass chaos in complexity.

Abstract

We present a heuristic analysis of the dynamics of general solutions to the Einstein Field Equations which highlights the possibility that such systems could possess a degree of unpredictability stronger than that which characterises chaotic systems. Questions regarding features of the complex dynamics of such cosmological models can be undecidable. These systems could be qualitatively compared with Turing machines in the sense that even if initial conditions for a dynamical system associated to general solutions to the Einstein Field Equations were known exactly, then the subsequent evolution could still be unpredictable.