Related papers: Stability of Stellar Systems Orbiting SgrA*
The orbital evolution and stability of planetary systems with interaction from the belts is studied using the standard phase-plane analysis. In addition to the fixed point which corresponds to the Keplerian orbit, there are other fixed…
We study the dynamical stability of planetary systems consisting of one hypothetical terrestrial mass planet ($1 $ or $10 \mearth$) and one massive planet ($10 \mearth - 10 \mjup$). We consider masses and orbits that cover the range of…
Gravitational stability of a disc consisting of the gaseous and the stellar components are studied in the linear regime when the gaseous component is turbulent. A phenomenological approach is adopted to describe the turbulence, in which not…
We analyze the behavior of the scalar field as dark energy of the Universe in a static world of galaxies and clusters of galaxies. We find the analytical solutions of evolution equations of the density and velocity perturbations of dark…
Locating the position of periodic orbits in galaxies is undoubtedly an issue of paramount importance. We reveal the position and the stability of periodic orbits of stars moving in the meridional plane $(R,z)$ of an axially symmetric…
Recent perturbative studies have shown the existence of long-lived, quasi-stationary configurations of scalar fields around black holes. In particular, such configurations have been found to survive for cosmological timescales, which is a…
In this review, I discuss just three aspects of the stability and evolution of galactic discs. (1) I first review our understanding of the bar instability and how it can be controlled. Disc galaxies in which the orbital speed does not…
These notes, based on lectures given at the summer school on Asymptotic Analysis in General Relativity, collect material on the Einstein equations, the geometry of black hole spacetimes, and the analysis of fields on black hole backgrounds.…
The singularity of the solutions obtained before in the teleparallel theory of gravitation is studied. Also the stability of these solutions is studied using the equations of geodesic deviation. The condition of stability is obtained. From…
We review the current state of dynamical modeling for galaxies in terms of being able to measure both the central black hole mass and stellar orbital structure. Both of these must be known adequately to measure either property. The current…
We examine bound orbits of particles around singly rotating black rings. We show that there exist stable bound orbits in toroidal spiral shape near the axis of the ring, and also exist stable circular orbits on the axis as special cases.…
Accurate modeling of gravitational interactions is fundamental to the analysis, prediction, and control of space systems. While the Newtonian point-mass approximation suffices for many preliminary studies, real celestial bodies exhibit…
We demonstrate that black holes and stars in general relativity can be destabilized by perturbations of non-minimally coupled vector fields. Focusing on static and spherically symmetric backgrounds, our analysis shows that black holes with…
The spacetime singularities play a useful role in gravitational theories by distinguishing physical solutions from non-physical ones. The problem, we studying in this paper is: are these singularities stable? To answer this question, we…
In co-orbital planetary systems, two or more planets share the same orbit around their star. Here we test the dynamical stability of co-orbital rings of planets perturbed by outside forces. We test two setups: i) 'stationary' rings of…
The origin of equilibrium gravitational configurations is sought in terms of the stability of their trajectories, as described by the curvature of their Lagrangian configuration manifold of particle positions --- a context in which subtle…
The stability of rotating isotropic spherical stellar systems is investigated by using N-body simulations. Four spherical models with realistic density profiles are studied: one of them fits the luminosity profile of globular clusters,…
The study of off-equatorial orbits in razor-thin disks is still in its beginnings. Contrary to what was presented in the literature in recent publications, the vertical stability criterion for equatorial circular orbits cannot be based on…
We examine the stability of a low-mass stellar system surrounding a massive central object. Examples of such systems include the centers of galaxies or star clusters containing a massive black hole, and the Oort comet cloud. If the…
We perform 3D numerical simulations in full general relativity to study the stability of rapidly rotating, supramassive neutron stars at the mass-shedding limit to dynamical collapse. We adopt an adiabatic equation of state with $\Gamma =…