Fractal basins and chaotic trajectories in multi-black hole space-times
N. J. Cornish, C. P. Dettmann, N. E. Frankel
TL;DR
This paper explores the complex dynamics of particle trajectories in multi-black hole spacetimes, revealing fractal basin boundaries and chaos characterized by Lyapunov exponents, advancing understanding of gravitational chaos.
Contribution
It demonstrates that chaotic geodesics in multi-black hole spacetimes can be quantitatively described using Lyapunov exponents and identifies fractal structures in the basin boundaries.
Findings
Chaotic geodesics are characterized by Lyapunov exponents.
Attractor basin boundaries exhibit fractal scaling.
Fractal basin boundaries are diffeomorphism invariant.
Abstract
We investigate the phase-space for trajectories in multi-black hole spacetimes. We find that complete, chaotic geodesics are well described by Lyapunov exponents, and that the attractor basin boundary scales as a fractal in a diffeomorphism invariant manner.
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