# 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

#### References

SHOWING 1-10 OF 47 REFERENCES

Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length

- Physics
- 2020

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 the… Expand

Numerical verification of the microscopic time reversibility of Newton's equations of motion: Fighting exponential divergence

- Computer Science, Physics
- Commun. Nonlinear Sci. Numer. Simul.
- 2018

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

- Physics
- 2013

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 in… Expand

Global chaoticity in the Pythagorean three-body problem

- Mathematics
- 1994

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

- Physics
- Astronomy & Astrophysics
- 2021

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

- Physics
- 2014

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 how… Expand

The Gravitational equations and the problem of motion

- Mathematics
- 1938

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. Previous… Expand

Round-off sensitivity in the N -body problem

- Mathematics
- 1986

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 deviations… Expand

Existence of collisional trajectories of Mercury, Mars and Venus with the Earth

- Physics, Medicine
- Nature
- 2009

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

- Physics, Medicine
- Living reviews in relativity
- 2014

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