相关论文: A Uniform Spherical Goat (Problem): Explicit Solut…
We continue our analysis of a quantum cosmology model describing a flat Friedmann--Lema\^itre--Robertson--Walker universe filled with a (free) massless scalar field and an arbitrary perfect fluid. For positive energy density in the scalar…
Deriving the time evolution of a distribution of probability (or a probability density matrix) is a problem encountered frequently in a variety of situations: for physical time, it could be a kinetic reaction study, while identifying time…
We construct an exact time-dependent solution in $D=4$, ${\cal N}=4$ gauged supergravity, where the gauge fields of the $U(1)\times U(1)$ subgroup of the $SO(4)$ carry independent conserved charges. The solution describes a decaying white…
This paper is about the $n+2$-dimensional gravitational contraction of inhomogeneous fluid without heat flux in the framework of $f(R)$ metric theory of gravity. Matching conditions for two regions of a star has been derived by using the…
A spherically symmetric collapsing scalar field model is discussed with a dissipative fluid which includes a heat flux. This vastly general matter distribution is analyzed at the expense of a high degree of symmetry in the space-time, that…
We show that the multi-dimensional compressible Euler system for isothermal flow of an ideal, polytropic gas admits global-in-time, radially symmetric solutions with unbounded amplitudes due to wave focusing. The examples are similarity…
We study the hydrodynamic self-similar mass collapses of general polytropic (GP) spherical clouds to central Schwarzschild black holes and void evolution with or without shocks. In order to grossly capture characteristic effects of general…
We present a class of singularity free exact cosmological solutions of Einstein's equations describing a perfect fluid with heat flow. It is obtained as generalization of the Senovilla class [1] corresponding to incoherent radiation field.…
In the supercritical range of the polytropic indices $\gamma\in(1,\frac43)$ we show the existence of smooth radially symmetric self-similar solutions to the gravitational Euler-Poisson system. These solutions exhibit gravitational collapse…
In this article, we present a gravitational collapse null dust solution of the Einstein field equations. The spacetime is regular everywhere except on the symmetry axis where it possesses a naked curvature singularity, and admits one…
Given the lack of an absolute time parameter in general relativistic systems, quantum cosmology often describes the expansion of the universe in terms of relational changes between two degrees of freedom, such as matter and geometry.…
Homogeneous fragmentations describe the evolution of a unit mass that breaks down randomly into pieces as time passes. They can be thought of as continuous time analogs of a certain type of branching random walks, which suggests the use of…
As per general relativity (GR), there cannot be any superluminal propagation of energy. And thus, the sound speed in a continuous medium, $c_s=\sqrt{dp/d\rho}$, must be subluminal. However, if one would conceive of a {\em homogeneous}…
We investigate the turnaround radius in the spherical collapse model, both in General Relativity and in modified gravity, in particular $f(R)$ scenarios. The phases of spherical collapse are marked by the density contrast in the instant of…
We consider Smoluchowski's coagulation equation in the case of the diagonal kernel with homogeneity $\gamma>1$. In this case the phenomenon of gelation occurs and solutions lose mass at some finite time. The problem of the existence of…
In this paper, we study the global existence, uniqueness and large-time behavior of spherically symmetric solution of a viscous radiative and reactive gas in an unbounded domain exterior to the unit sphere in $\mathbb{R}^{n}$ for $n\geq 2$.…
We revisit the classical problem of diffusion of a scalar (or heat) released in a two-dimensional medium with an embedded periodic array of impermeable obstacles such as perforations. Homogenisation theory provides a coarse-grained…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
We study the general properties of fluid spheres satisfying the heuristic assumption that their areas and proper radius are equal (the Euclidean condition). Dissipative and non-dissipative models are considered. In the latter case, all…
We investigate a simple inhomogeneous anisotropic cosmology (plane symmetric $G_2$ model) filled with a tilted perfect fluid undergoing velocity diffusion on a scalar field. Considered are two types of fluid: dust and radiation. We solve…