Related papers: Relativistic rigid systems and the cosmic expansio…
Cosmological N-Body simulations have become an essential tool for studying formation of large scale structure. These simulations are computationally challenging even though the available computing power gets better every year. A number of…
We consider a test of the Copernican Principle through observations of the large-scale structures, and for this purpose we study the self-gravitating system in a relativistic huge void universe model which does not invoke the Copernican…
We consider the motion of a two-dimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing…
Two questions are investigated by looking successively at classical mechanics, special relativity, and relativistic gravity: first, how is space related with spacetime? The proposed answer is that each given reference fluid, that is a…
We investigate a cosmological model resulting from a dimensional reduction of the higher-dimensional dRGT massive gravity. By using the Kaluza-Klein dimensional reduction, we obtain an effective four-dimensional massive gravity theory with…
Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…
The formation of the cosmic structures in the late Universe is considered using Vlasov kinetic approach. The crucial point is the use of the gravitational potential with repulsive term of the cosmological constant which provides a solution…
The notion of ``fundamental constant'' is heavily theory-laden. A natural, fairly precise formulation is possible in the context of the standard model (here defined to include gravity). Some fundamental constants have profound geometric…
Cosmological $N$-body simulations are the standard tool to study the emergence of the observed large-scale structure of the Universe. Such simulations usually solve for the gravitational dynamics of matter within the Newtonian…
The space expansion physics contains several paradoxes which were clearly demonstrated by Edward Harrison (1981, 1995, 2000), who emphasized that the cooling of homogeneous hot gas (including photon gas of CBR) in the standard cosmological…
Energy is at best defined quasilocally in general relativity. Quasilocal energy definitions depend on the conditions one imposes on the boundary Hamiltonian, i.e., how a finite region of spacetime is "isolated". Here, we propose a method to…
The Nobel Prize winning confirmation in 1998 of the accelerated expansion of our Universe put into sharp focus the need of a consistent theoretical model to explain the origin of this acceleration. As a result over the past two decades…
We present a brief history of the construction of models of the universe, followed by calculations of quantitative characteristics of basic geometric and kinematic properties of the Standard Cosmological Model ($\Lambda$CDM). Using the…
Unimodular relativity is a theory of gravity and space-time with a fixed absolute space-time volume element, the modulus, which we suppose is proportional to the number of microscopic modules in that volume element. In general relativity an…
In the framework of the special theory of relativity, the relativistic theory of gravitation (RTG) is constructed. The energy-momentum tensor density of all the matter fields (including gravitational one) is treated as a source of the…
Observations of distant supernovae indicate that the Universe is now in a phase of accelerated expansion the physical cause of which is a mystery. Formally, this requires the inclusion of a term acting as a negative pressure in the…
We discuss several topics related to the notion of strong hyperbolicity which are of interest in general relativity. After introducing the concept and showing its relevance we provide some covariant definitions of strong hyperbolicity. We…
We consider the proposition that multiple universes exist by reviewing the various manifestations. In recent years, this idea has been elevated from science fiction and introduced in separate guises as an explanation for coincidence…
The luminosity distance-redshift relation is one of the fundamental tools of modern cosmology. We compute the luminosity distance-redshift relation in a perturbed flat matter-dominated Universe, taking into account the presence of…
In this thesis, multipole expansions of mass, momentum and stress density will be made for a body in Newtonian mechanics. Using these definitions; momentum, angular momentum, center of mass, force and torque are defined for $N$…