Related papers: Uniformly Rotating Homogeneous Rings in Newtonian …
In this paper, we first describe how we can arrange any bodies on Figure-Eight without collision in a dense subset of $[0,T]$ after showing that the self-intersections of Figure-Eight will not happen in this subset. Then it is reasonable…
The homogeneous weights and the M\"obius functions and Euler phi-functions on finite rings are discussed; some computational formulas for these functions on finite principal ideal rings are characterized; for the residue rings of integers,…
Exact stationary axially symmetric solutions of the 4D Einstein equations with corotating pressureless perfect fluid sources are studied. A particular solution with approximately flat rotation curve is discussed in some detail. We find that…
Consider a smooth manifold $M$. Let $G$ be a compact Lie group which acts on $M$ with cohomogeneity one. Let $Q$ be a singular orbit for this action. We study the gradient Ricci soliton equation $\Hess(u)+\Ric(g)+\frac{\epsilon}{2}g=0$…
We present solutions to the Einstein-Klein Gordon system representing boson stars in the slow rotation approximation. By considering slow rotation we are able to reduce the number of equations yielding a system of ordinary differential…
Nonminimal spin-gravity interaction through unit gravimagnetic moment leads to modified Mathisson-Papapetrou-Tulczyjew-Dixon equations with improved behavior in the ultrarelativistic limit. We present exact Hamiltonian of the resulting…
Non-Euclidean triangle centers can be described using homogeneous coordinates that are proportional to the generalized sines of the directed distances of a given center from the edges of the reference triangle. Identical homogeneous…
In this paper we consider the motion of a rotating black hole through a static, homogeneous, massless scalar field. In the general case, a constant vector of the field gradient can be timelike, spacelike or null. We consider and compare all…
We describe the quantum dynamics of a magnetic rigid rotor in the mesoscopic scale where the Einstein-De Haas effect is predominant. In particular, we consider a single-domain magnetic nanoparticle with uniaxial anisotropy in a magnetic…
We give a set of exact nonlinear closed--form solutions for the non-spherical collapse of pressure-less matter in Newtonian gravity, and indicate their possible cosmological applications. Keywords: Newtonian gravitation: free collapse,…
We present a formalism to obtain equilibrium configurations of uniformly rotating fluid in the second post-Newtonian approximation of general relativity. In our formalism, we need to solve 29 Poisson equations, but their source terms…
We study quantum radiation generated by a uniformly accelerated motion of small spherical mirrors. To obtain Green's function for a scalar massless field we use Wick's rotation. In the Euclidean domain the problem is reduced to finding an…
The Hamiltonian for a system of relativistic bodies interacting by their gravitational field is found in the post-Minkowskian approximation, including all terms linear in the gravitational constant. It is given in a surprisingly simple…
We consider a two-dimensional, incompressible fluid body, together with self-induced interactions. The body is perturbed by an external particle with small mass. The whole configuration rotates uniformly around the common center of mass. We…
A pseudo-Newtonian Hill problem based on a potential proposed by Artemova et al. [Astroph. J. 461 (1996) 565] is presented. This potential reproduces some of the general relativistic effects due to the spin angular momentum of the bodies,…
We present a procedure for averaging one-parameter random unitary groups and random self-adjoint groups. Central to this is a generalization of the notion of weak convergence of a sequence of measures and the corresponding generalization of…
Variational techniques have been used in applications of hydrodynamics in special cases but an action that is general enough to deal with both potential flows and solid-body flows, such as cylindrical Couette flow and rotating planets, has…
The Euler-Poisson equations para determinar the rotation matrix of a rigid body can be solved without using of particular parameterization like the Euler angles. For the free Lagrange top, we obtain and discuss a general analytic solution,…
We investigate the motion of a massless body interacting with the Maxwell relative equilibrium, which consists of n bodies of equal mass at the vertices of a regular polygon that rotates around a central mass. The massless body has three…
We present a novel method to study interacting orbits in a fixed mean gravitational field associated with a solution of the Einstein field equations. The idea is to consider the Newton gravity among the orbiting particles in a geometry…