相关论文: A Generalized approach for Approximate Solutions t…

We summarize a recent work done on the title's subject. First, we present the asymptotic scheme of post-Newtonian (PN) approximation for general relativity in the harmonic gauge. Then, we discuss the definition of the mass centers and the…

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,…

A method is presented to compute approximate solutions for eigenequations in quantum mechanics with an arbitrary kinetic part. In some cases, the approximate eigenvalues can be analytically determined and they can be lower or upper bounds.…

A surprising "duality" of the Newton equation with time-dependent forces and the stationary Schroedinger equation is discussed. Wide classes of exact solutions not known before for few-body Newton equations are generated directly from…

We search for spherically symmetric solutions of f(R) theories of gravity via the Noether Symmetry Approach. A general formalism in the metric framework is developed considering a point-like f(R)-Lagrangian where spherical symmetry is…

The present paper studies the post-Newtonian dynamics of N bodies in general relativity. We derive covariant equations of translational and rotational motion of N extended bodies having arbitrary distribution of mass and velocity of matter…

The gravitational interaction is scale-free in both Newtonian gravity and general theory of relativity. The concept of self-similarity arises from this nature. Self-similar solutions reproduce themselves as the scale changes. This property…

We consider an analytic way to make the interacting N-body problem tractable by using harmonic oscillators in place of the relevant two-body interactions. The two body terms of the N-body Hamiltonian are approximated by considering the…

We review a recent theoretical progress in the so-called self-force problem of a general relativistic two-body system. Although a two-body system in Newtonian gravity is a very simple problem, some fundamental issues are involved in…

Approximate equations are derived for the motion of a gyroscope on the earth's gravitational field using the Einstein, Infeld, Hoffmann surface integral method. This method does not require a knowledge of the energy-momentum-stress tensor…

The restricted planar four body problem describes the motion of a massless body under the Newtonian gravitational force of other three bodies (the primaries), of which the motion gives us general solutions of the three body problem. A…

Numerical N-body simulations of large scale structure formation in the universe are based on Newtonian gravity. However, according to our current understanding, the most correct theory of gravity is general relativity. It is therefore…

The aim of this paper is to study the motion of $2+n$-body problem where two equal masses are assumed to be fixed. We assume that the value of each fixed mass is equal to $M>0$ and the remaining $n$ moving particles have equal masses $m>0$.…

In contrast to the well-known solution of the two-body problem through the use of the concept of reduced mass, a solution is proposed involving separation of potentials. It is shown that each of the two point bodies moves in its own…

The restricted (equilateral) four-body problem consists of three bodies of masses m1, m2 and m3 (called primaries) lying in a Lagrangian config- uration of the three-body problem, i,e,. they remain fixed at the apices of an equilateral…

Laboratory experiments on gravitation are usually performed with objects of constant density, so that the analysis of the forces concerns only the geometry of their shape. In an ideal experiment, the shapes of the constituent parts will be…

In the frame of multifractal theory of time and space (in this model our universe is consisting of real time and space fields and is the multifractal universe) in the works [1]-[16] some problems were analyzed: how the fractional dimensions…

An action minimizing path between two given configurations, spatial or planar, of the $n$-body problem is always a true -- collision-free -- solution. Based on a remarkable idea of Christian Marchal, this theorem implies the existence of…

The two-body problem in General Relativity has been the subject of many analytical investigations. After reviewing some of the methods used to tackle this problem (and, more generally, the N-body problem), we focus on a new, recently…

Using the Euclidon method, a stationary solution of Einstein's vacuum equations was obtained, describing N rotating axially symmetric masses, which in the absence of rotation describes N arbitrary axially symmetric static masses, for…