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Three-body dynamics in a (1+1) -dimensional relativistic self-gravitating system
1Department of Physics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1. jjmaleck@uwaterloo.ca
Summary
We studied a three-particle system under general relativistic gravity. Changing particle masses alters phase space regions, revealing new chaotic dynamics beyond Newtonian approximations.
Area of Science:
- Astrophysics
- General Relativity
- Computational Physics
Background:
- Self-gravitating systems are fundamental in astrophysics.
- Understanding relativistic effects on multi-body dynamics is crucial.
Purpose of the Study:
- To analyze the dynamics of a three-particle system in general relativistic lineal gravity.
- To investigate the influence of arbitrary mass ratios on system behavior.
Main Methods:
- Derivation of a canonical Hamiltonian for the system.
- Numerical solutions of the equations of motion.
- Comparison with nonrelativistic and post-Newtonian approximations.
Main Results:
- Identified three distinct phase space regions: annulus, pretzel (quasiperiodic), and chaotic.
- Demonstrated that changing particle mass ratios alters the size of these regions.
- Observed additional chaotic regions in unequal mass systems.
Conclusions:
- Relativistic dynamics can be viewed as a correction to Newtonian systems.
- Particle mass ratios significantly impact the system's phase space structure and dynamics.
- Unequal mass systems exhibit richer chaotic behavior than equal mass systems.