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

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.