Related papers: PoMiN: A Post-Minkowskian $N$-Body Solver
The dynamics of compact binary systems at the fourth post-Newtonian (4PN) approximation of general relativity has been recently completed in a self-consistent way. In this paper, we compute the ten Poincar\'e constants of the motion and…
We revisit the dynamics of the post-Newtonian (PN) two-body problem for two inspiraling compact bodies. Starting from a matter-only reduced Hamiltonian, we present an adapted framework based on the Lie series approach, enabling the…
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…
This is the first in a series of papers devoted to fully general-relativistic $N$-body simulations applied to late-time cosmology. The purpose of this paper is to present the combination of a numerical relativity scheme, discretization…
We present a framework for general relativistic N-body simulations in the regime of weak gravitational fields. In this approach, Einstein's equations are expanded in terms of metric perturbations about a Friedmann-Lema\^itre background,…
Modified Newtonian dynamics (MOND) is a promising alternative to dark matter. To further test the theory, there is a need for fluid- and particle-dynamics simulations. The force in MOND is not a direct particle-particle interaction, but…
Using the post-Newtonian effective field theory (PN-EFT) formalism for spinning gravitating bodies, we derive the next-to-leading-order (NLO) spin-orbit potential and Hamiltonian for a system of N spinning bodies in general relativity. This…
A technique for translating the classical scattering function of two gravitationally interacting bodies into a corresponding (effective one-body) Hamiltonian description has been recently introduced [Phys.\ Rev.\ D {\bf 94}, 104015 (2016)].…
A novel approach to the Effective One-Body description of gravitationally interacting two-body systems is introduced. This approach is based on the post-Minkowskian approximation scheme (perturbation theory in G, without assuming small…
In the present paper, the leading-order post-Newtonian spin-orbit and spin(1)-spin(2) radiation-reaction Hamiltonians are calculated. We utilize the canonical formalism of Arnowitt, Deser, and Misner (ADM), which has shown to be valuable…
We developed a Keplerian-based Hamiltonian splitting for solving the gravitational $N$-body problem. This splitting allows us to approximate the solution of a general $N$-body problem by a composition of multiple, independently evolved…
This dissertation consists of four parts. In Part I, we briefly review fundamental theories of gravity, performed experimental tests, and gravitational waves. The framework and the methods that we use in our calculations are discussed in…
The regular-geometric-figure solution to the $N$-body problem is presented in a very simple way. The Newtonian formalism is used without resorting to a more involved rotating coordinate system. Those configurations occur for other kinds of…
Several completely integrable, indeed solvable, Hamiltonian many-body problems are exhibited, characterized by Newtonian equations of motion ("acceleration equal force"), with linear and cubic forces, in N-dimensional space (N being an…
We report on the first fully consistent conventional cluster simulation which includes terms up to post^{5/2} Newtonian in the potential of the massive body. Numerical problems for treating extremely energetic binaries orbiting a single…
We consider the two-body problem in post-Newtonian approximations of general relativity. We report the recent results concerning the equations of motion, and the associated Lagrangian formulation, of compact binary systems, at the third…
We extend the systematic calculation of an approximately relativistic Hamiltonian for centre of mass and internal dynamics of an electromagnetically bound two-particle system by Sonnleitner and Barnett [1] to the case including a weak…
Several N-body problems in ordinary (3-dimensional) space are introduced which are characterized by Newtonian equations of motion (``acceleration equal force;'' in most cases, the forces are velocity-dependent) and are amenable to exact…
We consider an application of the Multipolar Post Minkowskian formalism to the case of a two-body system in radial fall. We compute, within the post-Newtonian approximation, the associated gravitational waveform reaching the 2.5…
Here we present a new particle-mesh galactic N-body code that uses the full multigrid algorithm for solving the modified Poisson equation of the Quasi Linear formulation of Modified Newtonian Dynamics (QUMOND). A novel approach for handling…