Related papers: Lagrange point stability for a rotating host mass …
In this paper we have examined the linear stability of triangular equilibrium points in the generalised photogravitational restricted three body problem with Poynting-Robertson drag. We have found the position of triangular equilibrium…
Despite the existence of co-orbital bodies in the solar system, and the prediction of the formation of co-orbital planets by planetary system formation models, no co-orbital exoplanets (also called trojans) have been detected thus far. In…
The three-body problem is famously chaotic, with no closed-form analytical solutions. However, hierarchical systems of three or more bodies can be stable over indefinite timescales. A system is considered hierarchical if the bodies can be…
We show that a massive black hole binary might resonantly trap a small third body (e.g. a neutron star) down to a stage when the binary becomes relativistic due to its orbital decay by gravitational radiation. The final fate of the third…
Designing for rotational stability can dramatically affect the geometry of a space station. If improperly designed, the rotating station could end up catastrophically tumbling end-over-end. Active stabilization can address this problem;…
We establish a criterion for the stability of planetary orbits in stellar binary systems by using Lyapunov exponents and power spectra for the special case of the circular restricted 3-body problem (CR3BP). The centerpiece of our method is…
We extend earlier discussions of the balance problem for two black holes and study stationary spacetimes containing an arbitrary number of $n$ aligned rotating and (possibly) charged black holes. For these hypothetical equilibrium…
The evolution of small perturbations around rotating black branes and strings, which are low energy solutions of string theory, are investigated. For simplicity, we concentrate on the Kerr solution times transverse flat extra dimensions,…
We consider the motion of massive and massless particles in a five-dimensional spacetime with a compactified extra-dimensional space where a black hole is localized, i.e., a caged black hole spacetime. We show the existence of circular…
For the linear baryon string model with three massive points (three quarks) connected sequentially by the relativistic strings the initial-boundary value problem is stated and solved in general. This problem implies defining a classical…
The multi-dissipative photogravitational triaxial elliptic restricted three body problem is treated. The perturbed locations of triangular points are computed. The stability of the triangular points under changing one or more perturbing…
We derive the secular evolution of the orbital elements of a stellar-mass object orbiting a spinning massive black hole. We use the post-Newtonian approximation in harmonic coordinates, with test-body equations of motion for the…
The circular restricted three body problem, which considers the dynamics of an infinitesimal particle in the presence of the gravitational interaction with two massive bodies moving on circular orbits about their common center of mass, is a…
We show that transient resonances occur in the two body problem in general relativity, in the highly relativistic, extreme mass-ratio regime for spinning black holes. These resonances occur when the ratio of polar and radial orbital…
Spin precession occurs in binary black holes whose spins are misaligned with the orbital angular momentum. Otherwise, the spin configuration is constant and the subsequent binary dynamics and gravitational-wave emission are much simpler. We…
We establish the evolution equations of the set of independent variables characterizing the 2PN rigorous conservative dynamics of a spinning compact binary, with the inclusion of the leading order spin-orbit, spin-spin and mass quadrupole -…
This paper describes design of the trajectory and analysis of the stability of collinear point $L_2$ in the Sun-Earth system. The modified restricted three body problem with additional gravitational potential from the belt is used as the…
In dynamical systems of few degrees of freedom, periodic solutions consist the backbone of the phase space and the determination and computation of their stability is crucial for understanding the global dynamics. In this paper we study the…
It is an interesting open problem whether two non-extremal rotating and electrically charged black holes can be in physical equilibrium, which might be possible due to a balance between the gravitational attraction and the spin-spin and…
In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…