Mutual Information for particle pair and its application to diagnose Chaos in Curved Spacetime

TL;DR

This paper introduces a new mutual information-based method for diagnosing chaos in particle pairs within curved spacetime, demonstrating its effectiveness in identifying orbital states and transitions in Schwarzschild and Kerr spacetimes.

Contribution

The paper proposes the mutual information for particle pairs (MIPP) as a novel chaos indicator applicable to curved spacetime, expanding the tools for analyzing dynamical systems in general relativity.

Findings

MIPP effectively identifies orbital states.

MIPP outperforms the fast Lyapunov indicator in certain scenarios.

Information theory enhances understanding of few-body dynamics.

Abstract

We propose the concept of mutual information for particle pair (MIPP) in curved spacetime, and show that MIPP has potential to be a proper chaos indicator. We tested this method in the Schwarzschild and Kerr spacetime and compared it with the fast Lyapunov indicator. The results show that the MIPP effectively identify orbital states and demonstrates prominent performance in recognizing transitions between orbital states. Our result show that information theory significantly deepen our understanding of dynamics of few-body system.