相关论文: A Uniform Spherical Goat (Problem): Explicit Solut…
In this paper, we study permutation symmetric solutions of the incompressible Euler equation. We show that the dynamics of these solutions can be reduced to an evolution equation on a single vorticity component $\omega_1$, and we…
We propose a new approximation-technique to deal with the exact macroscopic integro-differential evolution equations of statistical systems which self-consistently accounts for dissipative effects. Concentrating on one and two point…
We perform radiation hydrodynamical simulations of protostellar collapse in spherical symmetry, with a special focus on very low-mass objects, i.e. brown dwarfs and sub-brown dwarfs. The inclusion of a realistic equation of state that…
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…
The present paper concerns a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of corrector results (i.e., strong convergences of…
Various types of inhomogeneous collapse models in general relativity (GR) lead to the formation of spacetime singularities either visible or hidden by a spacetime horizon. Our aim in the present work is to search for nonsingular models in…
Context. The composition of a protoplanetary disk at a given location does not only depend on temperature and pressure but also on the time dependent transport of matter, such as radial drift of solid bodies, which could release water and…
Spherically symmetric solutions in F(R) theories in astronomical systems with rising energy density are studied. The range of parameters is established for which the flat space-time approximation for the background metric is valid. For the…
The short-time and global behaviour are studied for an autonomous linear evolution equation, which is defined by a generator inducing a uniformly bounded holomorphic semigroup in a Hilbert space. A general necessary and sufficient condition…
We present semi-analytical solutions to the background equations describing the Lema\^itre-Tolman-Bondi (LTB) metric as well as the homogeneous Friedmann equations, in the presence of dust, curvature and a cosmological constant Lambda. For…
We investigate self-similar scalar field solutions to the Einstein equations in whole cylinder symmetry. Imposing self-similarity on the spacetime gives rise to a set of single variable functions describing the metric. Furthermore, it is…
We study the spherical gravitational collapse of a compact object under the approximation that the radial pressure is identically zero, and the tangential pressure is related to the density by a linear equation of state. It turns out that…
We develop a spherical self-similar model for the formation of a galaxy through gas collapsing in an isolated self-gravitating dark matter halo. We improve upon the existing literature on self-similar collapse in two ways. First, we include…
The timescape cosmology represents a potentially viable alternative to the standard homogeneous cosmology, without the need for dark energy. Although average cosmic evolution in the timescape scenario only differs substantially from that of…
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…
An analytical method is presented for treating the problem of a uniformly rotating, self-gravitating ring without a central body in Newtonian gravity. The method is based on an expansion about the thin ring limit, where the cross-section of…
This paper examines the temporal evolution of a two-stage stochastic model for spherical random fields. The model uses a time-fractional stochastic hyperbolic diffusion equation, which describes the evolution of spherical random fields on…
The process of gravitational collapse excites the fields propagating in the background geometry and gives rise to thermal radiation. We demonstrate by explicit calculations that the density matrix corresponding to such radiation actually…
We consider four-dimensional Einstein gravity minimally coupled to a dilaton scalar field with a supergravity-inspired scalar potential. We obtain an exact time-dependent spherically symmetric solution describing gravitational collapse to a…
A partially alternative derivation of the expression for the time dilation effect in a uniform static gravitational field is obtained by means of a thought experiment in which rates of clocks at rest at different heights are compared using…