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The motion of a rigid, spinning disk on a flat surface ends with a dissipation-induced finite-time singularity. The problem of finding the dominant energy absorption mechanism during the last phase of the motion generated a lively debate…

An infinite family of relativistic finite thin disk model with magnetic field is presented. The model is obtained for solving the Einstein-Maxwell equations for static spacetimes by means of the Horsk\'y-Mitskievitch generating conjecture.…

We describe a family of circular, and elliptical, finite disks with a disk potential that is a power of the radius. These are all flattened ellipsoids, obtained by squashing finite spheres with a power-law density distribution, and cutoff…

The observation of the motion of particles and light near a gravitating object is until now the only way to explore and to measure the gravitational field. In the case of exact black hole solutions of the Einstein equations the…

The relationship between the geometrical properties of stellar disks (a flatness and truncation radius) and the disk kinematics are considered for edge-on galaxies. It is shown that the observed thickness of the disks and the approximate…

A self-consistent solution for a thin accretion disk with turbulent convection is presented. The disk viscosity and the convective flux are derived from a physical model for turbulence, and expressed in terms of the local physical…

The stationary hydrodynamic equations for transonic viscous accretion discs in Kerr geometry are derived. The consistent formulation is given for the viscous angular momentum transport and the boundary conditions on the horizon of a central…

The process of gravitational accretion of initially homogeneous gas onto a solid ball is studied with methods of fluid dynamics. The fluid partial differential equations for polytropic flow can be solved exactly in an early stage, but this…

We apply two theoretical and two numerical methods to the problem of a disk placed in a groove and subjected to gravity and a torque. Methods assuming rigid particles are indeterminate -- certain combinations of forces cannot be calculated,…

A thin gaseous disk has often been investigated in the context of various phenomena in galaxies, which point to the existence of starburst rings and dense circumnuclear molecular disks. The effect of self-gravity of the gas in the 2D disk…

We find a family of exact solutions of Einstein equations describing the field of a static axisymmetric thin disk living in six-dimensional space-time. In particular, we study the disks constructed (by cutting out the central part of the…

We investigate the relationship between rigid motions and relative equilibria in the N-body problem on the two-dimensional sphere, S2. We prove that any rigid motion of the N-body system on S2 must be a relative equilibrium. Our approach…

We find a new method for looking for the static and spherically symmetric solutions in $F(R)$ theory of gravity. With this method, a number of new solutions in terms of the analytic functions are obtained. We hope this investigation may be…

Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…

In this study, we develop a simplified magnetofluid model in the framework of GRMHD. We consider an ideal, adiabatic fluid composed of two components, ions and electrons, having a constant ratio between their temperatures. The flows are…

This paper studies the main features of the dynamics around a massive annular disk. The first part addresses the difficulties finding an appropriated expression of the gravitational potential of a massive disk, which will be used to define…

We study the observational properties of a class of exact solutions of Einstein's field equations describing stationary, axially symmetric, rigidly rotating dust (i.e. non interacting particles). We ask the question whether such solutions…

The viscous evolution of a thin disc around a central object is considered. Such discs are described by self-similar solutions in which either all or none of the inflowing mass accretes. An approximate solution for the partial accretion…

The measured rotation velocity profiles of mature spiral galaxies are successfully described with a gravitational model consisting of a thin axisymmetric disk of finte radius. The disk is assumed uniformly thin but with variable radial mass…

We consider the basic physical properties of matter forming a thin accretion disc in the static and spherically symmetric space-time metric of the vacuum $f(R)$ modified gravity models. The Lagrangian of the generalized gravity theory is…