Related papers: Kinematic Self-Similarity
D-dimensional cosmological model describing the evolution of a perfect fluid with negative pressure (x-fluid) and a fluid possessing both shear and bulk viscosity in n Ricci-flat spaces is investigated. The second equations of state are…
We review a recently proposed definition of complexity of the structure of self--gravitating fluids \cite{ch1}, and the criterium to define the simplest mode of their evolution. We analyze the origin of these concepts and their possible…
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…
Asymptotics of solutions of a perfect fluid when coupled with a cosmological constant in four-dimensional spacetime with toroidal symmetry are studied. In particular, it is found that the problem of self-similar solutions of the first kind…
An analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta…
The dynamics of a spinning fluid in a flat cosmological model is investigated. The space-time is itself generated by the spinning fluid which is characterized by an energy-momentum tensor consisting a sum of the usual perfect-fluid…
Models of turbulent flows require the resolution of a vast range of scales, from large eddies to small-scale features directly associated with dissipation. As the required resolution is not within reach of large scale numerical simulations,…
The Einstein equations for a perfect fluid spatially homogeneous spacetime are studied in a unified manner by retaining the generality of certain parameters whose discrete values correspond to the various Bianchi types of spatial…
We classify all spherically symmetric and homothetic spacetimes that are allowed kinematically by constructing them from a small number of building blocks. We then restrict attention to a particular dynamics, namely perfect fluid matter…
In Newtonian physics, the excitation spectrum of a fluid is the same in all reference frames, up to a trivial shift. In special relativity, this is no longer the case. Relativity of simultaneity causes different inertial observers to…
A method of solving perfect fluid Einstein equations with two commuting spacelike Killing vectors is presented. Given a spacelike 2-dimensional surface in the 3-dimensional nonphysical Minkowski space the field equations reduce to a single…
Exact solutions with an exponential behaviour of the scale factors are considered in a multidimensional cosmological model describing the dynamics of n+1 Ricci-flat factor spaces M_i in the presence of a one-component perfect fluid. The…
We study the evolution of an anisotropic shear-free fluid with heat flux and kinematic self-similarity of the second kind. We found a class of solution to the Einstein field equations by assuming that the part of the tangential pressure…
We consider the motion of several rigid bodies immersed in a two-dimensional incompress-ible perfect fluid, the whole system being bounded by an external impermeable fixed boundary. The fluid motion is described by the incompressible Euler…
In this article, we first investigate the kinematics of specific geodesic flows on two dimensional media with constant curvature, by explicitly solving the evolution (Raychaudhuri) equations for the expansion, shear and rotation along the…
We develop a geometric formulation of fluid dynamics, valid on arbitrary Riemannian manifolds, that regards the momentum-flux and stress tensors as 1-form valued 2-forms, and their divergence as a covariant exterior derivative. We review…
In the last century, theoretical and experimental developments have established the General Relativity theory as the most successful theory for describing the gravitational phenomenon. On the other hand, in the last two decades, multiple…
We introduce a formulation of Eulerian general relativistic hydrodynamics which is applicable for (perfect) fluid data prescribed on either spacelike or null hypersurfaces. Simple explicit expressions for the characteristic speeds and…
An exact solution of the Einstein field equations is found under the assumption of spherically symmetry and the existence of one-parameter group of homothetic motions. This solution has a singularity at $r = 0$, and has non-vanishing…
We study the classical and quantum models of a Friedmann-Robertson-Walker (FRW) cosmology, coupled to a perfect fluid, in the context of the $f(R)$ gravity. Using the Schutz' representation for the perfect fluid, we show that, under a…