Chaos in the relativistic Euler problem.

Area of Science:

• Astrophysics
• General Relativity
• Computational Physics

Background:

• The classical Euler problem involves three bodies, with two fixed and one moving mass.
• General relativity effects on particle dynamics around massive objects are crucial for understanding gravitational interactions.
• Previous studies may not have fully explored the chaotic nature of scattering in such systems.

Purpose of the Study:

• To reconsider the Euler problem within the framework of general relativity.
• To investigate the scattering dynamics of a particle interacting with two fixed black holes.
• To identify and analyze signs of chaotic behavior in particle trajectories.

Main Methods:

• Numerical computation of particle trajectories.
• Utilizing a modified muffin tin approximation for calculations.
• Analysis of scattering angle versus impact parameter plots.

Main Results:

• The scattering of a particle by two neutral, fixed black holes exhibits strong chaotic behavior.
• Distinct signs of chaos were observed in the computed particle trajectories.
• The relationship between scattering angle and impact parameter clearly indicates chaotic dynamics.

Conclusions:

• The Euler problem, when extended by general relativity and involving two black holes, demonstrates significant chaotic scattering.
• Numerical simulations provide evidence for the chaotic nature of particle interactions in this astrophysical scenario.
• The findings contribute to the understanding of complex gravitational dynamics and chaos theory.