General Relativistic Effects on Hill Stability of Multi-Body Systems I: Stability of Three-Body Systems Containing a Massive Black Hole
arXiv:2009.06999 · doi:10.1103/PhysRevD.102.124063
Abstract
We study the effects of general relativistic gravity on the Hill stability, that is, the stability of a multi-body system against a close approach of one orbit to another, which has been hitherto studied mainly in Newtonian mechanics and applied to planetary systems. We focus in this paper on the three-body problem and extend the Newtonian analyses to the general relativistic regime in the post-Newtonian approximation. The approximate sufficient condition for the relativistic Hill stability of three-body systems is derived analytically and its validity and usefulness are confirmed numerically. In fact, relativity makes the system more unstable than Newtonian mechanics in the sense of the Hill stability as expected by our theoretical prediction. The criterion will be useful to analyze the results of large-scale N-body simulations of dense environments, in which the stability of three-body sub-systems is important.
arXiv comment16 pages, 10 figures, accepted for publication in Physical Review D
References in corpus (31)
- Dynamical Outcomes of Planet-Planet Scattering
- The Kozai Mechanism and the Evolution of Binary Supermassive Black Holes
- The Formation of Eccentric Compact Binary Inspirals and the Role of Gravitational Wave Emission in Binary-Single Stellar Encounters
- A millisecond pulsar in a stellar triple system
- Eccentric Black Hole Mergers in Dense Star Clusters: The Role of Binary-Binary Encounters
- Orbital Migration of Interacting Stellar Mass Black Holes in Disks around Supermassive Black Holes
- Post-Oligarchic Evolution of Protoplanetary Embryos and the Stability of Planetary Systems
- On the rate of black hole binary mergers in galactic nuclei due to dynamical hardening
- Tidal resonance in extreme mass-ratio inspirals
- On incorporating post-Newtonian effects in N-body dynamics
- Spin-Orbit Misalignment of Merging Black-Hole Binaries with Tertiary Companions
- Generalized Hill-Stability Criteria for Hierarchical Three-Body Systems at Arbitrary Inclinations
- Detecting Supermassive Black Hole-Induced Binary Eccentricity Oscillations with LISA
- Eccentricity and Spin-Orbit Misalignment in Short-Period Stellar Binaries as a Signpost of Hidden Tertiary Companions
- Binary Mergers near a Supermassive Black Hole: Relativistic Effects in Triples
- A Direct Probe of Mass Density Near Inspiraling Binary Black Holes
- Dynamical behaviour of multiplanet systems close to their stability limit
- Eccentric binary black hole mergers in globular clusters hosting intermediate-mass black holes
- Gravitational Waves from Hierarchical Triple Systems with Kozai-Lidov Oscillation
- Orbital Stability of Multi-Planet Systems: Behavior at High Masses
- Impact of a Spinning Supermassive Black Hole on the Orbit and Gravitational Waves of a Nearby Compact Binary
- Post-Newtonian effects in N-body dynamics: Relativistic precession and conserved quantities in hierarchical triple systems
- The Keplerian three-body encounter II. Comparisons with isolated encounters and impact on gravitational wave merger timescales
- The Keplerian three-body encounter I. Insights on the origin of the S-stars and the G-objects in the Galactic center
- Massive binary star mergers in galactic nuclei: implications for blue stragglers, binary S-stars and gravitational waves
- The butterfly effect in the extreme-mass ratio inspiral problem
- The non-resonant, relativistic dynamics of circumbinary planets
- Secular evolution of compact binaries revolving around a spinning massive black hole
- Interrupted Binary Mass Transfer in Star Clusters
- Post-Newtonian Kozai-Lidov Mechanism and its Effect on Cumulative Shift of Periastron Time of Binary Pulsar
- Cumulative Shift of Periastron Time of Binary Pulsar with Kozai-Lidov Oscillation
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