Relativistic Pythagorean three-body problem
نویسندگان
چکیده
We study the influence of relativity on chaotic properties and dynamical outcomes an unstable triple system; Pythagorean three-body problem. To this end, we extend brutus N-body code to include post-Newtonian pairwise terms up 2.5 order, first order Taylor expansion Einstein-Infeld-Hoffmann equations motion. The degree which our system is relativistic depends scaling total mass (the unit size was 1 parsec). Using method convergence, test for time-reversibility in conservative regime, demonstrate that are able obtain definitive solutions It also confirmed minimal required numerical accuracy a successful correlates with amplification factor initial perturbation, as found previously Newtonian case. When take into account dissipative effects through gravitational wave emission, find duration resonance, amount exponential growth small perturbations depend scaling. For $\ensuremath{\le}10\text{ }\text{ }{\mathrm{M}}_{\ensuremath{\bigodot}}$, behavior indistinguishable from Newton's motion, resonance always ends binary one escaping body. ${10}^{7}\text{ gradually becomes more prominent, but majority systems still dissolve single body isolated binary. mergers start appear $\ensuremath{\sim}{10}^{5}\text{ between }{\mathrm{M}}_{\ensuremath{\bigodot}}$ ${10}^{9}\text{ all end prematurely merger. These preceded by driven in-spiral. $\ensuremath{\ge}{10}^{9}\text{ result merger upon close encounter. Relativistic encounters thus provide efficient pathway resolving final parsec onset at characteristic scale potentially leaves imprint function supermassive black holes.
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ژورنال
عنوان ژورنال: Physical review
سال: 2021
ISSN: ['0556-2813', '1538-4497', '1089-490X']
DOI: https://doi.org/10.1103/physrevd.104.083020