Relativistic Pythagorean three-body problem

@article{Boekholt2021RelativisticPT,
  title={Relativistic Pythagorean three-body problem},
  author={Tjarda Boekholt and Arend Moerman and Simon F. Portegies Zwart},
  journal={Physical Review D},
  year={2021}
}
We study the influence of relativity on the chaotic properties and dynamical outcomes of an unstable triple system; the Pythagorean three-body problem. To this end, we extend the Brutus N-body code to include Post-Newtonian pairwise terms up to 2.5 order, and the first order Taylor expansion to the Einstein-Infeld-Hoffmann equations of motion. The degree to which our system is relativistic depends on the scaling of the total mass (the unit size was 1 parsec). Using the Brutus method of… Expand

Figures and Tables from this paper

References

SHOWING 1-10 OF 47 REFERENCES
Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length
Chaos is present in most stellar dynamical systems and manifests itself through the exponential growth of small perturbations. Exponential divergence drives time irreversibility and increases theExpand
Numerical verification of the microscopic time reversibility of Newton's equations of motion: Fighting exponential divergence
TLDR
It is demonstrated that when numerical errors are reduced to below the physical perturbation and its exponential growth during integration the microscopic reversibility is retrieved. Expand
RESONANT POST-NEWTONIAN ECCENTRICITY EXCITATION IN HIERARCHICAL THREE-BODY SYSTEMS
We study the secular, hierarchical three-body problem to first-order in a post-Newtonian expansion of general relativity (GR). We expand the first-order post-Newtonian Hamiltonian to leading-order inExpand
Global chaoticity in the Pythagorean three-body problem
The effects of small changes in the initial conditions of the Pythagorean three-body problem are investigated by computer simulations. This problem consists of three interacting bodies with masses 3,Expand
Chaos in self-gravitating many-body systems. Lyapunov time dependence of N and the influence of general relativity
In self-gravitating N-body systems, small perturbations introduced at the start, or infinitesimal errors that are produced by the numerical integrator or are due to limited precision in the computer,Expand
Incorporating post-Newtonian effects in N-body dynamics
The increasing role of general relativity in the dynamics of stellar systems with central massive black holes and in the evolution of hierarchical triple systems inspires a close examination of howExpand
The Gravitational equations and the problem of motion
Introduction. In this paper we investigate the fundamentally simple question of the extent to which the relativistic equations of gravitation determine the motion of ponderable bodies. PreviousExpand
Round-off sensitivity in the N -body problem
The solutions to the equations of motion of the gravitational N-body problem are extremely sensitive to very small changes in initial conditions, resulting in a near-exponential growth of deviationsExpand
Existence of collisional trajectories of Mercury, Mars and Venus with the Earth
TLDR
Numerical simulations of the evolution of the Solar System over 5 Gyr, including contributions from the Moon and general relativity find that one per cent of the solutions lead to a large increase in Mercury’s eccentricity—an increase large enough to allow collisions with Venus or the Sun. Expand
Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries
  • L. Blanchet
  • Physics, Medicine
  • Living reviews in relativity
  • 2014
TLDR
The current state of the art on post-Newtonian methods as applied to the dynamics and gravitational radiation of general matter sources (including the radiation reaction back onto the source) and inspiralling compact binaries is presented. Expand
...
1
2
3
4
5
...