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

In this talk we show a stiff fluid solution of the Einstein equations for a cylindrically symmetric spacetime. The main features of this metric are that it is non-separable in comoving coordinates for the congruence of the worldlineS of the…

After the original discovery of the Kerr metric, Newman and Janis showed that this solution could be ``derived'' by making an elementary complex transformation to the Schwarzschild solution. The same method was then used to obtain a new…

We search for spherically symmetric solutions of f(R) theories of gravity via the Noether Symmetry Approach. A general formalism in the metric framework is developed considering a point-like f(R)-Lagrangian where spherical symmetry is…

In a recent series of papers new exact analytical solutions of the field equations of General Relativity representing interior spacetimes sourced by stationary rigidly rotating cylinders of fluids with various equations of state have been…

Interior perfect fluid solutions for the Reissner-Nordstrom metric are studied on the basis of a new classification scheme. It specifies which two of the fluid's characteristics are given functions and picks up accordingly one of the three…

Here, we derive the metric for the spacetime around rotating object for the gravity action having nonlocal correction of $R\Box^{-2} R $ to the Einstein-Hilbert action. Starting with the generic stationary, axisymmetric metric, we solve the…

Static spherically symmetric perfect fluid solutions are studied in metric $f(R)$ theories of gravity. We show that pressure and density do not uniquely determine $f(R)$ ie. given a matter distribution and an equation state, one cannot…

Lie symmetry group method is applied to study Newtonian incompressible fluid's equations flow in turbulent boundary layers. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are…

We show that under particular circumstances a general relativistic spherically symmetric bounded distribution of matter could satisfy a nonlocal equation of state. This equation relates, at a given point, the components of the corresponding…

We study the spherically symmetric collapse of a perfect fluid using area-radial coordinates. We show that analytic mass functions describe a static regular centre in these coordinates. In this case, a central singularity can not be…

Via a straightforward integration of the Einstein equations with cosmological constant, all static circularly symmetric perfect fluid 2+1 solutions are derived. The structural functions of the metric depend on the energy density, which…

Newman-Janis algorithm for Kerr-Newman geometry is reanalyzed in the light of Cartan calculus.

We review analytical solutions of the Einstein equations which are expressed in terms of elementary functions and describe Friedmann-Lema\^itre-Robertson-Walker universes sourced by multiple (real or effective) perfect fluids with constant…

In this paper a fluid-structure interaction problem for the incompressible Newtonian fluid is studied. We prove the convergence of an iterative process with respect to the computational domain geometry. In our previous works on numerical…

The nonlinear equations describing all the nonsingular pencils of metrics of constant Riemannian curvature are derived and the integrability of these nonlinear equations by the method of inverse scattering problem is proved. It is proved…

Einstein's equations of General Relativity form a highly nonlinear system, so most exact solutions rely on symmetry assumptions. Spherically symmetric spacetimes have been particularly important, providing a tractable yet physically rich…

In the present paper we analyze and discuss some mathematical aspects of the fluid-static configurations of a self-gravitating perfect gas enclosed in a spherical solid shell. The mathematical model we consider is based on the well-known…

We present a matrix method for obtaining new classes of exact solutions for Einstein's equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein's equations to two independent Riccati type…

A main issue in cosmology and astrophysics is whether the dark sector phenomenology originates from particle physics, then requiring the detection of new fundamental components, or it can be addressed by modifying General Relativity.…

A double new class of solutions to the general relativity field equations describing interior spacetimes sourced by stationary cylindrical anisotropic fluids with principal stress directed along the symmetry axis is displayed. These…