Related papers: Relativistic Mean Motion Resonance
We study the dynamics of a hierarchical three-body system in the general-relativistic regime: an extreme mass-ratio inner binary under the tidal influence of an external body. The inner binary consists of a central Schwarzschild black hole…
A model of three-body motion is developed which includes the effects of gravitational radiation reaction. The radiation reaction due to the emission of gravitational waves is the only post-Newtonian effect that is included here. For…
Stars around a massive black hole (MBH) move on nearly fixed Keplerian orbits, in a centrally-dominated potential. The random fluctuations of the discrete stellar background cause small potential perturbations, which accelerate the…
In this article, we explore both numerically and analytically how the dynamical environments of mildly relativistic binaries evolve with increasing the general relativity factor $\gamma$ (the normalized inverse of the binary size measured…
Inspirals of stellar mass compact objects into supermassive black holes are known as extreme mass ratio inspirals. In the simplest approximation, the motion of the compact object is modeled as a geodesic in the space-time of the massive…
We examine a 2DOF Hamiltonian system, which arises in study of first-order mean motion resonance in spatial circular restricted three-body problem "star-planet-asteroid", and point out some mechanisms of chaos generation. Phase variables of…
We investigate the (conservative) dynamics of binary black holes using the Hamiltonian formulation of the post-Newtonian (PN) equations of motion. The Hamiltonian we use includes spin-orbit coupling, spin-spin coupling, and mass…
We present, in closed analytic form, a general stationary, slowly rotating black hole, which is solution to a large class of alternative theories of gravity in four dimensions. In these theories, the Einstein-Hilbert action is supplemented…
The traditional approach to analyzing mean motion resonances is through canonical perturbation theory. While this is a powerful method, its generality leads to complicated combinations of variables that are challenging to interpret and…
Mean motion resonances (MMRs) can lead either to chaotic or regular motion. We report on a numerical experiment showing that even in one of the most chaotic regions of the Solar System - the region of the giant planets, there are numerous…
In this paper the effects of vibrations at high frequencies onto a freely falling two-body system in Schwarzschild spacetime are investigated. As reference motion of the same system without vibrations a circular orbit around the central…
Mean motion commensurabilities in multi-planet systems are an expected outcome of protoplanetary disk-driven migration, and their relative dearth in the observational data presents an important challenge to current models of planet…
This paper focuses on two-planet systems in a first-order $(q+1):q$ mean motion resonance and undergoing type-I migration in a disc. We present a detailed analysis of the resonance valid for any value of $q$. Expressions for the equilibrium…
Mean motion resonances are important in the analysis and understanding of the dynamics of planetary systems. While perturbative approaches have been dominant in many previous studies, recent non-perturbative approaches have revealed novel…
A Hamiltonian that approaches the study of the three-body problem in general relativity is obtained. We use it to study the relativistic version of the circular restricted three-body problem in which the first body is the heaviest and the…
Asteroids in mean motion resonances with giant planets are common in the solar system, but it was not until recently that several asteroids in retrograde mean motion resonances with Jupiter and Saturn were discovered. A retrograde…
Following the general numerical analysis of Melita and Woolfson (1996), I showed in a recent paper that a restricted, planar, circular planetary system consisting of Sun, Jupiter and Saturn would be captured in a near (2:1) resonance when…
We summarize the analytic model and numerical simulations of stochastically forced planets in a turbulent disk presented in a recent paper by Rein and Papaloizou. We identify two modes of libration in systems with planets in mean motion…
We develop a framework based on energy kicks for the evolution of high-eccentricity long-period orbits with Jacobi constant close to 3 in the restricted circular planar three-body problem where the secondary and primary masses have mass…
We present the first exploration of relativistic gas dynamics in the immediate vicinity of binary black holes as the system inspirals close to merger in the gravitational radiation-driven regime. We focus on 2D hydrodynamical studies of…