Related papers: Numerical integration of a relativistic two-body p…
The quantum mechanical many-body problem is rarely analytically solvable. One notable exception is the case of two electrons interacting via a Coulomb potential in a uniform magnetic field. The motion is confined to a two-dimensional plane,…
The worldlines (in harmonic coordinates) of two gravitationally interacting massive bodies at the second post-Minkowskian order are described in explicit form. Both the conservative case and the radiation-reacted case are considered. We use…
The importance and usefulness of renormalization are emphasized in nonrelativistic quantum mechanics. The momentum space treatment of both two-body bound state and scattering problems involving some potentials singular at the origin…
Gravitational waves provide a new probe into the strong-field regime of gravity. It is thus essential to identify the predictions of General Relativity on the nature of the two-body problem, and to contrast them to alternative theories.…
The existence of stationary distributions in a multicomponent Boltzmann equation using a non-additive kinetic energy composition rule for binary collisions is discussed. It is found that detailed balance is not achieved when -- in contrast…
The orbital motion of inspiralling and coalescing black hole binaries can be investigated using a variety of approximation schemes and numerical methods within general relativity: post-Newtonian expansions, black hole perturbation theory,…
In a previous paper (Gayon & Bois 2008a), we have shown the general efficiency of retrograde resonances for stabilizing compact planetary systems. Such retrograde resonances can be found when two-planets of a three-body planetary system are…
In this paper we study the linear stability of relative equilibria in the Newtonian $n$-body problem from the viewpoint of electromagnetic systems. We first examine the effect of the ambient dimension on stability, starting from the…
The problem of the description of two interacting particles is considered. It is shown that it can be reduced to the description of one particle in an external static potential even in a relativistic case. The method is based on the…
This study presents a general alternative scheme of the procedure and necessary conditions for solving the $n$-body problem. The presented solution is not a solution of the classical problem, where the initial conditions of positions and…
The two body problem in a scalar theory of gravity is investigated. We focus on the closest theory to General Relativity (GR), namely Nordstr\"om's theory of gravity (1913). The gravitational field can be exactly solved for any…
We survey theoretical and experimental/observational results on general-relativistic spin (rotation) effects in binary systems. A detailed discussion is given of the two-body Kepler problem and its first post-Newtonian generalization,…
We discuss a new N-body simulation method for studying black hole binary dynamics. This method avoids previous numerical problems due to large mass ratios and trapped orbits with short periods. A treatment of relativistic effects is…
The consideration of dynamics of relativistic beams/particles is based on variational approach to rational (in dynamical variables) approximation for equations of motions. It allows to control contribution from each scale of underlying…
We derive a first order formalism for solving the scattering of point sources in (2+1) gravity with negative cosmological constant. We show that their physical motion can be mapped, with a polydromic coordinate transformation, to a trivial…
We present a systematic post-Newtonian treatment of binary charged black holes immersed in external magnetic fields within the framework of Einstein-Maxwell theory. By incorporating a uniform external magnetic field into the two-body…
In the present paper, using the first-order approximation of the $n$-body Lagrangian (derived on the basis of the post-Newtonian gravitational theory of Einstein, Infeld, and Hoffman), we explicitly write down the equations of motion for…
Natural orbital theory is a computationally useful approach to the few and many-body quantum problem. While natural orbitals are known and applied since many years in electronic structure applications, their potential for time-dependent…
Relativistic systems of particles interacting pairwise at a distance (interactions not mediated by fields) in flat spacetime are studied. It is assumed that the interactions propagate at the speed of light in vacuum and that all masses are…
We consider the Kepler two-body problem in the presence of a cosmological constant Lambda. Several dimensionless parameters characterizing the possible orbit typologies are used to identify open and closed trajectories. The qualitative…