Related papers: The general static spherical perfect fluid solutio…
This paper deals with isothermal Euler-Poisson system which is used to model collapse of self-gravitating Newtonian star. Density dependent viscosity term is added on the right-hand side of momentum equation and it has been proved that…
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…
We present a solution of the quantum mechanics problem of the allowable energy levels of a bound particle in a one-dimensional finite square well. The method is a geometric-analytic technique utilizing the conformal mapping $w \to z = w…
General exact (N+2)-dimensional,n>=2 solutions in general theory of relativity of Einstein-Maxwell field equations for static anisotropic spherically symmetric distribution of charged fluid are expressed in terms of radial pressure.…
We investigate all static spherically symmetric solutions in the context of general relativity surrounded by a minimally-coupled quintessence field, using dynamical system analysis. Applying the 1+1+2 formalism and introducing suitable…
We present a new system of equations that fully characterizes adiabatic, radial perturbations of perfect fluid stars within the theory of general relativity. The properties of the system are discussed, and, provided that the equilibrium…
Recently, an exact spherically symmetric analytic accretion solution was presented having simple $\rho \propto R^{-3/2}$ and $V \propto R^{-1/2}$ scalings in Hernandez et al. (2023). In dimensionless variables that solution forms a…
This is the first of two papers examining the critical collapse of spherically symmetric perfect fluids with the equation of state P = (Gamma -1)rho. Here we present the equations of motion and describe a computer code capable of simulating…
An explicit necessary condition for the occurrence of resonance scattering of axial gravitational waves, along with the internal trapping of null geodesics, is proposed for static spherically symmetric perfect fluid solutions to Einstein's…
We consider the asymptotically flat standing wave solutions to the Poisson-Schr\"{o}dinger system of equations known as static states. These solutions can be parameterized using a variety of choices of two continuous parameters and one…
It is necessary for the statistical description of collective effects in liquids to set that or other approximation between direct and pair correlation functions which describe a neighboring order. The analytical solution of the generalized…
In recent years, experimental data were published which point to the possibility of the existence of superfluidity in solid helium. To investigate this phenomenon theoretically we employ a hierarchy of equations for reduced density matrices…
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…
The spherical capillary water waves equation describes the motion of an almost spherical water droplet under zero gravity governed by water-air interface tension. Using para-differential calculus on compact Lie groups and homogeneous spaces…
Based on the asymptotic analysis of ordinary differential equations, we classify all spherically symmetric self-similar solutions to the Einstein equations which are asymptotically Friedmann at large distances and contain a perfect fluid…
In the present article, we discuss relativistic anisotropic solutions of the Einstein field equation for the spherically symmetric line element under the class I condition. To do so we apply the embedding class one technique using Eisland…
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…
Analyzing the spacetime for a static spherically distributed perfect fluid we show that the smooth matching of the interior and exterior metrics for a realistic source is possible only for the distances from the origin that exceeds the…
We take up the investigation we left in the future-work stack in Giordano \textit{et al.} [``Fluid statics of a self-gravitational isothermal sphere of van der Waals' gas,'' Phys. Fluids \textbf{36}, 056127 (2024)], in which we pointed out…
Starting from a general transformation for spherically symmetric metrics where g\_11=-1/g\_00, we analyze coordinates with the common property of conformal flatness at constant solid angle element. Three general possibilities arise: one…