Related papers: Gravitational potential of a homogeneous circular …

This paper deals with the gravitational potential of a homogeneous torus with elliptical cross-section. We present a new expression for its gravitational potential which is valid in any point of the space, obtained by modeling the torus…

New exact solutions are derived for the gravitational potential inside and outside a homogeneous torus as rapidly converging series of toroidal harmonics. The approach consists of splitting the inter- nal potential into a known solution to…

We perform a bivariate Taylor expansion of the axisymmetric Green function in order to determine the exterior potential of a static thin toroidal shell having a circular section, as given by the Laplace equation. This expansion, performed…

We have investigated the toroidal analog of ellipsoidal shells of matter, which are of great significance in Astrophysics. The exact formula for the gravitational potential $\Psi(R,Z)$ of a shell with a circular section at the pole of…

We have established the exact expression for the gravitational potential of a homogeneous polar cell - an elementary pattern used in hydrodynamical simulations of gravitating discs. This formula, which is a closed-form, works for any…

Gravitational potential and gravitational energy are presented in analytical form for homogeneous rectangular parallelepiped.

I developed an efficient numerical method for obtaining the gravitational potential of razor-thin spiral perturbations and used it to assess the standard tight-winding approximation, which is found to be reasonably accurate for pitch angles…

It is shown that the gravitational potential outside an inhomogeneous ellipsoid of revolution (spheroid) whose isodensity surfaces are confocal spheroids is identical to the gravitational potential of a homogeneous spheroid of the same…

We study the properties of the Newtonian gravitational potential in a spherical Universe for different topologies. For this, we use the non-Euclidean Newtonian theory developed in Vigneron [2022, Class. & Quantum Gravity, 39, 155006]…

The gravitational-wave spectrum emitted by a non-axisymmetric torus rotating at an angular velocity $\Omega_T$, is derived in terms of a structure function representing a combination of sausage-tilt modes in the torus in the limit of an…

The motion in a simple, time independent rational galactic potential is studied. The potential is a generalization of a two dimensional harmonic oscillator potential and can be considered to describe plane motion in the central parts of a…

The Schrodinger equation for an electron on the surface of an elliptical torus in the presence of a constant azimuthally symmetric magnetic field is developed. The single particle spectrum and eigenfunctions as a function of magnetic flux…

We investigate a potential obtained as the convolution of a radially symmetric function and the characteristic function of a body (the closure of a bonded open set) with exterior cones. In order to restrict the location of a maximizer of…

The local character of self-gravity along with the number of spatial dimensions are critical issues when computing the potential and forces inside massive systems like stars and disks. This appears from the discretisation scale where each…

Ring galaxies are amazing objects exemplified by the famous case of the Hoag's Object. Here the mass of the central galaxy may be comparable to the mass of the ring, making it a difficult case to model mechanically. In a previous paper, it…

Gravitational potential energy of the homogeneous bispherical concavo-convex lens, with the equal absolute values of radii of curvature of both surfaces is studied.

In the spirit of the thin-layer quantization scheme, we give the effective Shr\"{o}dinger equation for a particle confined to a corrugated torus, in which the geometric potential is substantially changed by corrugation. We find the…

We give an integral expression for the vector potential of a time-independent, steady azimuthal current density. Our derivation is substantially simpler and somewhat more general than others given in the literature. As an illustration, we…

The gravitational properties of a torus are investigated. It is shown that a torus can be formed from test particles orbiting in the gravitational field of a central mass. In this case, a toroidal distribution is achieved because of the…

By using various properties of the complete elliptic integrals, we have derived an alternative expression for the gravitational potential of axially symmetric bodies, which is free of singular kernel in contrast with the classical form.…