Related papers: Lagrange point stability for a rotating host mass …
After a brief introduction to the black hole stability problem, we outline our recent proof of the linear stability of the non-extreme Kerr geometry.
We extend the notion of orbital stability to systems of nonlinear Schrodinger equations, then we prove this property under suitable assumptions of the local nonlinearity involved.
The Lidov-Kozai mechanism allows a body to periodically exchange its eccentricity with inclination. It was first discussed in the framework of the quadrupolar secular restricted three-body problem, where the massless particle is the inner…
In order to perform model-dependent tests of general relativity with gravitational wave observations, we must have access to numerical relativity binary black hole waveforms in theories beyond general relativity (GR). In this study, we…
The current early stage in the investigation of the stability of the Kerr metric is characterized by the study of appropriate model problems. Particularly interesting is the problem of the stability of the solutions of the Klein-Gordon…
Mean motion resonances are commonly seen in planetary systems, e.g., in the formation of orbital structure of Jupiter's moons and the gaps in the rings of Saturn. In this work we study their effects in fully relativistic systems. We…
We explore the classical stability of topological black holes in d-dimensional anti-de Sitter spacetime, where the horizon is an Einstein manifold of negative curvature. According to the gauge invariant formalism of Ishibashi and Kodama,…
The stability of a system of $N$ equal sized mutually gravitating spheres resting on each other in a straight line and rotating in inertial space is considered. This is a generalization of the "Euler Resting" configurations previously…
We study the stability under linear odd-parity perturbations of static spherically symmetric black holes in Horndeski gravity. We derive the master equation for these perturbations and obtain the conditions of no-ghost and Laplacian…
The existence of equilibrium points and the effect of radiation pressure have been discussed numerically. The problem is generalized by considering bigger primary as a source of radiation and small primary as an oblate spheroid. We have…
The vast majority of massive binary systems in the universe is evidently unsuited to produce merging binary black holes. However, several narrow evolutionary paths of isolated massive binaries towards this goal have recently been…
For a body with negligible mass moving in the gravitational field of a star and one planet in a circular orbit (the circular restricted three-body problem) five equilibrium points exist and are known as the Lagrangian points. The positions…
We study the linear stability of regular $n$-gon rotating equilibria in the $n$-body problem with logarithm interaction. In the presence of a central mass $M$, linear stability is insured if $M$ is bounded below and above by constants…
The stability of the Lagrangian point $L_4$ is investigated in the elliptic restricted three-body problem by using Floquet's theory. Stable and unstable domains are determined in the parameter plane of the mass parameter and the…
We study the orbital stability of a non-zero mass, close-in circular orbit planet around an eccentric orbit binary for various initial values of the binary eccentricity, binary mass fraction, planet mass, planet semi--major axis, and planet…
Recent studies of accretion onto supermassive black hole binaries suggest that much, perhaps most, of the matter eventually accretes onto one hole or the other. If so, then for binaries whose inspiral from ~1 pc to 0.001 - 0.01 pc is driven…
The theoretical description of compact structures that share some key features with mass varying particles allows for a simple analysis of equilibrium and stability for massive stellar bodies. We investigate static, spherically symmetric…
This study investigates the problem of areostationary orbits around Mars in the three-dimensional space. Areostationary orbits are expected to be used to establish a future telecommunication network for the exploration of Mars. However, no…
The Restricted 3-Body Problem models the motion of a body of negligible mass under the gravitational influence of two massive bodies called the primaries. If one assumes that the primaries perform circular motions and that all three bodies…
We study the Gregory-Laflamme instability of a 5-dimensional slowly rotating black string in which the 4-dimensional section is described by the Kerr black hole. We treat the rotation in a perturbative way introducing a small parameter for…