Related papers: On a weak solution of Einstein equations for expan…
We investigate the occurrence and nature of a naked singularity in the gravitational collapse of an inhomogeneous dust cloud described by a self-similar higher dimensional Tolman-Bondi space-time. Bound, marginally bound and unbound…
The two dark sectors of the universe - dark matter and dark energy - may interact with each other. Background and linear density perturbation evolution equations are developed for a generic coupling. We then establish the general conditions…
We aim at proving existence of weak solutions to the stationary compressible Navier-Stokes system coupled with the Allen-Cahn equation. The model is studied in a bounded three dimensional domain with slip boundary conditions for the…
We revisit the gravitational collapse of spherically symmetric Lema\^itre - Tolman - Bondi (LTB) dust models. A sufficient condition for global visibility of singularity is given. This condition also allows us to extend the condition of…
We study a class of time dependent solutions of the vacuum Einstein equations which are plane waves with weak null singularities. This singularity is weak in the sense that though the tidal forces diverge at the singularity, the rate of…
The standard model of cosmology with postulated dark energy and dark matter sources may be considered as a fairly successful fitting model to observational data. However, this model leaves the question of the physical origin of these dark…
We analyze here the issue of local versus the global visibility of a singularity that forms in gravitational collapse of a dust cloud, which has important implications for the weak and strong versions of the cosmic censorship hypothesis. We…
Conventional Cold Dark Matter cosmological models predict small scale structures, such as cuspy halos, which are in apparent conflict with observations. Several alternative scenarios based on modifying fundamental properties of the dark…
In the context of dark energy solutions, we consider a Friedmann-Robertson-Walker spacetime filled with a non-interacting mixture of dust and a viscous fluid, whose bulk viscosity is governed by the nonlinear model proposed in [15]. Through…
It is shown that a weak modification of general relativity, in the linearized approach, renders a spherically symmetric and stationary model of the universe. This is due to the presence of a third mode of polarization in the linearized…
We provide a new existence result for weak solutions to the one-dimensional Euler equations with a maximal density constraint, corresponding to a unilateral constraint on the density. Such models arise in the description of congestion…
There is a deep interrelationship of the General Theory of Relativity and weak interactions in the model of Expansive Nondecelerative Universe. This fact allows an independent determination of the mass of vector bosons Z and W, as well as…
We give a comparative description of monopole and electrically charged spherically symmetric dust thin shells. Herewith we consider two of the most interesting configurations: the hollow shell and shell, surrounding a body with opposite…
We study a Q-tensor problem modeling the dynamic of nematic liquid crystals in 3D domains. The system consists of the Navier-Stokes equations, with an extra stress tensor depending on the elastic forces of the liquid crystal, coupled with…
We analyse spherically symmetric spacetimes obtained by gluing a cosmological region to a Schwarzschild black hole across a singular co-dimension one hypersurface. Assuming an arbitrary homogeneous and isotropic cosmology, and working in…
We perform canonical analysis of a model in which gravity is coupled to a spherically symmetric dust shell in 2+1 spacetime dimensions. The result is a reduced action depending on a finite number of degrees of freedom. The emphasis is made…
We provide a covariant framework to study singularity-free Lema\^itre-Tolman-Bondi spacetimes with effective corrections motivated by loop quantum gravity. We show that, as in general relativity, physically reasonable energy distributions…
We study a model for a fluid showing viscoelastic and viscoplastic behavior, which describes the flow in terms of the fluid velocity and an internal stress. This stress tensor is transported via the Zaremba--Jaumann rate, and it is subject…
The Schwarzchild solution insertion in an expanding universe, the so-called "Swiss cheese model," is shown to possess a very unphysical property. Specifically, in this model some trajectories are discontinuous functions of their initial…
In the model where the Universe is considered as a thin shell expanding in 5-dimensional hyper-space there is a possibility to obtain one scale for particle theory corresponding to the 5-dimensional cosmological constant and Universe…