Related papers: Oscillating about coplanarity in the 4 body proble…
The spacetime homogeneous G\"odel-type spacetimes which have four classes of metrics are studied according to their matter collineations. The obtained results are compared with Killing vectors and Ricci collineations. It is found that these…
We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…
This paper investigates the critical behaviors of the 4-dimensional spinfoam model with cosmological constant for a general 4-dimensional simplicial complex as the discretization of spacetime. We find that, at the semi-classical regime, the…
A nonlinear fourth-order parabolic equation in one space dimension with periodic boundary conditions is studied. This equation arises in the context of fluctuations of a stationary nonequilibrium interface and in the modeling of quantum…
This paper is devoted to the study of matter collineations of plane symmetric spacetimes (for a particular class of spacetimes) when the energy-momentum tensor is non-degenerate. There exists many interesting cases where we obtain proper…
We prove that any simple planar travelling wave solution to the membrane equation in spatial dimension $d \geq 3$ with bounded spatial extent is globally nonlinearly stable under sufficiently small compactly-supported perturbations, where…
The continuous 1D defects of an isotropic homogeneous material in a flat 3D space are classified by the Volterra process construction method. We employ the same method to classify the continuous 2D defects of a vacuum in a 4D maximally…
We consider the $n$ body problem defined on surfaces of constant positive curvature. For the 5 and 7 body problem in a collinear symmetric configuration we obtain initial positions which lead to relative equilibria. We give explicitly the…
We study the problem of minimal resistance for a body moving with constant velocity in a rarefied medium of chaotically moving point particles, in Euclidean space R^d. The particles distribution over velocities is radially symmetric. Under…
In an earlier paper \cite{yu2021Finiteness}, we showed that there are finitely many stationary configurations (consisting of equilibria, rigidly translating configurations, relative equilibria and collapse configurations) in the planar…
We investigate matter collineations of plane symmetric spacetimes when the energy-momentum tensor is degenerate. There exists three interesting cases where the group of matter collineations is finite-dimensional. The matter collineations in…
We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in…
The self-force problem---which asks how self-interaction affects a body's motion---has been poorly studied for spacetime dimensions $d \neq 4$. We remedy this for all $d \geq 3$ by nonperturbatively constructing momenta such that forces and…
We investigate the equal-mass 3-body system in general relativistic lineal gravity in the presence of a cosmological constant $\Lambda$. The cosmological vacuum energy introduces features that do not have a non-relativistic counterpart,…
This paper investigates the coplanar and circular three-body problem in the parametrized post-Newtonian (PPN) formalism, for which we focus on a class of fully conservative theories characterized by the Eddington-Robertson parameters…
Our idea is to imitate Smale's list of problems, in a restricted domain of mathematical aspects of Celestial Mechanics. All the problems are on the n-body problem, some with different homogeneity of the potential, addressing many aspects…
The momentum space zero-range model is used to investigate universal properties of three interacting particles confined to two dimensions. The pertinent equations are first formulated for a system of two identical and one distinct particle…
Using a metric conformal formulation of the Einstein equations, we develop a construction of 4-dimensional anti-de Sitter-like spacetimes coupled to tracefree matter models. Our strategy relies on the formulation of an initial-boundary…
In this paper, we consider the elliptic collinear solutions of the classical $n$-body problem, where the $n$ bodies always stay on a straight line, and each of them moves on its own elliptic orbit with the same eccentricity. Such a motion…
We introduce an algebraic method to study local stability in the Newtonian $n$-body problem when certain symmetries are present. We use representation theory of groups to simplify the calculations of certain eigenvalue problems. The method…