Computation of Lyapunov Exponents in General Relativity

Abstract

Lyapunov exponents (LEs) are key indicators of chaos in dynamical systems. In general relativity the classical definition of LE meets difficulty because it is not coordinate invariant and spacetime coordinates lose their physical meaning as in Newtonian dynamics. We propose a new definition of relativistic LE and give its algorithm in any coordinate system, which represents the observed changing law of the space separation between two neighboring particles (an 'observer' and a 'neighbor'), and is truly coordinate invariant in a curved spacetime.

13 pages, 3 figures

References in corpus (7)

• Chaos in Schwarzschild Spacetime : The Motion of a Spinning Particle
• Gravity Waves, Chaos, and Spinning Compact Binaries
• Dynamical Chaos in the Wisdom-Holman Integrator: Origins and Solutions
• Ruling Out Chaos in Compact Binary Systems
• Relativistic and Newtonian core-shell models: analytical and numerical results
• Chaos around the superposition of a black-hole and a thin disk
• Chaos in Pseudo-Newtonian Black Holes with Halos

Cited by in corpus (47)

• Lyapunov indices with two nearby trajectories in a curved spacetime
• Numerical integration of variational equations
• Chaos and dynamics of spinning particles in Kerr spacetime
• Chaotic motion of particles in the accelerating and rotating black holes spacetime
• Particle Dynamics Near Kerr-MOG Black Hole
• Resurvey of order and chaos in spinning compact binaries
• Free motion around black holes with discs or rings: between integrability and chaos - I
• Chaos of Particle Motion near the Black Hole with Quasi-topological Electromagnetism
• Revisit on "Ruling out chaos in compact binary systems"
• Free motion around black holes with discs or rings: between integrability and chaos - III
• A Symmetric Integrator for non-integrable Hamiltonian Relativistic Systems
• Chaos from the ring string in Gauss-Bonnet black hole in $Ad{S}_5$ space
• Chaos in two black holes with next-to-leading order spin-spin interactions
• Second post-Newtonian Lagrangian dynamics of spinning compact binaries
• Applying explicit symplectic integrator to study chaos of charged particles around magnetized Kerr black hole
• Chaotic scalar fields as models for dark energy
• Chaos in self-gravitating many-body systems: Lyapunov time dependence of $N$ and the influence of general relativity
• Homoclinic orbit and the violation of the chaos bound around a black hole with anisotropic matter fields
• On the conservation of the Jacobi integral in the post-Newtonian circular restricted three-body problem
• Lyapunov exponent ISCO and Kolmogorov Senai entropy for Kerr Kiselev black hole
• Beyond-Newtonian dynamics of a planar circular restricted three-body problem with Kerr-like primaries
• Electromagnetic field and chaotic charged-particle motion around hairy black holes in Horndeski gravity
• Stability and chaos of hierarchical three black hole configurations
• Extended phase-space symplectic-like integrators for coherent post-Newtonian Euler-Lagrange equations
• A novel energy-conserving scheme for eight-dimensional systems
• Chaotic dynamics of string around charged black brane with hyperscaling violation
• Equivalence between two charged black holes in dynamics of orbits outside the event horizons
• A note on the equivalence of Lagrangian and Hamiltonian formulations at post-Newtonian approximations
• Effect of noncircularity on the dynamic behaviors of particles in a disformal rotating black-hole spacetime
• Oblique magnetic fields and the role of frame dragging near rotating black hole
• Chaotic motion of scalar particle coupling to Chern-Simons invariant in Kerr black hole spacetime
• Energy-conserving integrator for conservative Hamiltonian systems with ten-dimensional phase space
• Causality bounds chaos in geodesic motions
• Circular string in a Black p-brane leading to chaos
• Effects of Two Quantum Correction Parameters on Chaotic Dynamics of Particles Near Renormalized Group Improved Schwarzschild Black Holes
• A differential algorithm for the Lyapunov spectrum
• Impact of electric charges on chaos in magnetized $Reissner-Nordstr\ddot{o}m$ spacetimes
• Effects of coupling constants on chaos of charged particles in the $Einstein-\AE$ ther theory
• Mutual Information for particle pair and its application to diagnose Chaos in Curved Spacetime
• Chaotic motion of particles around a dyonic Kerr-Newman black hole immersed in the Melvin-swirling universe
• Screen chaotic motion by Shannon entropy in curved spacetimes
• On geodesic dynamics in deformed black-hole fields
• f(R) Gravity, relic coherent gravitons and optical chaos
• Time-reversed Shannon entropy as a chaos indicator for non-integrable systems
• Chaotic dynamics of charged particles near weakly magnetized black holes in Einstein-ModMax Theory
• GPU accelerated manifold correction method for spinning compact binaries
• A new correction method for quasi-Keplerian orbits