Related papers: Breakdown of self-similar evolution in homogeneous…
Static spherically symmetric solutions of the Einstein's field equations in isotropic coordinates representing perfect fluid matter distributions from Newtonian potential-density pairs are investigated. The approach is illustrated with…
This paper deals with the study of collapsing plane symmetric source in the presence of heat flux. For this purpose, we have calculated the Einstein field equations as well as Weyl tensor components. The conditions for the conformal…
The inhomogeneous cosmological model with matter in the form self-acting scalar field and perfect fluid is considered. On the basis of exact solutions is considered the evolution of density distribution of a matter in space on a background…
This paper deals with the collapse and expansion of relativistic anisotropic self-gravitating source. The field equations for non-radiating and non-static plane symmetric anisotropic source have been evaluated. The non-radiating property of…
In this paper we consider a system of equations that describes a class of mass-conserving aggregation phenomena, including gravitational collapse and bacterial chemotaxis. In spatial dimensions strictly larger than two, and under the…
Completing a previous analysis started in [1], we study flat Friedmann--Lema\^{\i}tre--Robertson--Walker (FLRW) models with a perfect fluid matter source and a scalar field nonminimally coupled to matter, self--interacting with a potential…
We present the full set of evolution equations for the spatially homogeneous cosmologies of type VI$_h$ filled with a tilted perfect fluid and we provide the corresponding equilibrium points of the resulting dynamical state space. It is…
We generalize the spherical collapse model for the formation of bound objects to apply in a Universe with arbitrary positive cosmological constant. We calculate the critical condition for collapse of an overdense region and give exact…
We show the existence of a new class of initially smooth spherically symmetric self-similar solutions to the non-isentropic Euler-Poisson system. These solutions exhibit supersonic gravitational implosion in the sense that the density…
Understanding the formation of binary and multiple stellar systems largely comes down to studying the circumstances for the fragmentation of a condensing core during the first stages of the collapse. However, the probability of…
We simulate the evolution of one-dimensional gravitating collisionless systems from non- equilibrium initial conditions, similar to the conditions that lead to the formation of dark- matter halos in three dimensions. As in the case of 3D…
In this note, we investigate the stability of self-similar blow-up solutions for superconformal semilinear wave equations in all dimensions. A central aspect of our analysis is the spectral equivalence of the linearized operators under…
Self similarity allows for analytic or semi-analytic solutions to many hydrodynamics problems. Most of these solutions are one dimensional. Using linear perturbation theory, expanded around such a one-dimensional solution, we find…
We study different dimensional fluids inspired by noncommutative geometry which admit conformal Killing vectors. The solutions of the Einstein field equations examined specifically for five different set of spacetime. We calculate the…
Gravitational collapse in (n+2) dimensional quasi-spherical space-time is studied for a fluid with non vanishing radial pressure. An exact analytic solution is obtained (ignoring the arbitrary integration function) for the equation of state…
We consider a collapsing sphere and discuss its evolution under the vanishing expansion scalar in the framework of $f(R)$ gravity. The fluid is assumed to be locally anisotropic which evolves adiabatically. To study the dynamics of the…
We investigate the structure of cold dark matter halos using advanced models of spherical collapse and accretion in an expanding Universe. These base on solving time-dependent equations for the moments of the phase-space distribution…
This paper is concerned with the figures of equilibrium of a self-gravitating ideal fluid with density stratification and a steady-state velocity field. As in the classical setting, it is assumed that the figures or their layers uniformly…
We study nonlinear stability of spatially homogeneous oscillations in reaction-diffusion systems. Assuming absence of unstable linear modes and linear diffusive behavior for the neutral phase, we prove that spatially localized perturbations…
We compare the gravitational collapse of homogeneous perfect fluid with various equations of state in the framework of General Relativity and in $R^2$ gravity. We make our calculations using dimensionless time with characteristic timescale…