相关论文: Rotating metrics admitting non-perfect fluids in G…

We introduce a technique to solve numerically the relativistic Euler's equations in scenarios with spherical symmetry using the standard Smoothed Particles Hydrodynamics method in cartesian coordinates. This implementation allow us to…

We analyze the field equations for the perfect fluid solutions admitting a group G$_3$ of isometries acting on orbits S$_2$ whose curvature has a gradient that is tangent to the fluid flow (T-models). We propose several methods to integrate…

A general class of solutions of Einstein's equation for a slowly rotating fluid source, with supporting internal pressure, is matched using Lichnerowicz junction conditions, to the Kerr metric up to and including first order terms in…

A global model of a slowly rotating perfect fluid ball in general relativity is presented. To second order in the rotation parameter, the junction surface is an ellipsoidal cylinder. The interior is given by a limiting case of the Wahlquist…

Many researches show that the complicated motion of fluid, such as turbulence, cannot be well solved by the Navier-Stokes equation. Chen Zida has founded that the definition of vortex, based on the Stokes decomposition, cannot well describe…

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…

The aim of this paper is to find higher order geometrical corrections to the Einstein-Hilbert action that can lead to only second order equations of motion. The metric formalism is used, and static spherically symmetric and…

We revisit the geodesic approach to ideal hydrodynamics and present a related geometric framework for Newton's equations on groups of diffeomorphisms and spaces of probability densities. The latter setting is sufficiently general to include…

We study the gravitational behaviour of a spherically symmetric radiating star when the fluid particles are in geodesic motion. We transform the governing equation into a simpler form which allows for a general analytic treatment. We find…

In the present paper we have discussed the mechanics of incompressible test bodies moving in Riemannian spaces with non-trivial curvature tensors. For Hamilton's equations of motion the solutions have been obtained in the parametrical form…

We find a new class of exact solutions for rotating black holes in $f(R)$ gravity in presence of imperfect fluid. We find that the exact solutions are holographically dual to a hidden conformal field theory. Moreover we consider another…

A general form of a metric preserving all symmetries of a spherically symmetric gravitational field and angular momentum in spherical coordinates is obtained. Such metric may have $g_{01}(r)\neq 0$. The Newtonian limit uniquely defines…

We revisit the problem of the rotating generalization of the Fisher-Janis-Newman-Winicour solution of the minimal Einstein-scalar theory proving that the two previously proposed solutions do not satisfy the equations of motion. We also…

In this work, we derive the general solutions for a cylindrically symmetric space-time filled with a cosmological perfect fluid obeying $p=\gamma \rho$ ($0\leq \gamma \leq 1$), where $\gamma=1$ represents a stiff or Zeldovich fluid. Using…

It is shown that the kinematic system describing planar non-steady motions of ideal fibre-reinforced fluids may be reduced to a single two-dimensional third-order partial differential equation in which time enters parametrically. A…

We discuss several approaches to generalized solutions of problems describing the motion of inviscid fluids. We propose a new concept of dissipative solution to the compressible Euler system based on a careful analysis of possible…

One field of fluid dynamics concerns the search for variational principles. So far, the Hamiltonian view and Riemannian geometry has been applied to find geodesics for hydrodynamic systems. Compared to Riemannian geometry sub-Riemannian…

An algorithm presented by K. Lake to obtain all static spherically symmetric perfect fluid solutions was recently extended by L. Herrera to the interesting case of locally anisotropic fluids (principal stresses unequal). In this work we…

Matrix geometric means between two positive definite matrices can be defined from distinct perspectives - as solutions to certain nonlinear systems of equations, as points along geodesics in Riemannian geometry, and as solutions to certain…

We investigate the conformal geometry of spherically symmetric spacetimes in general without specifying the form of the matter distribution. The general conformal Killing symmetry is obtained subject to a number of integrability conditions.…