Related papers: Relativistic virial relation for cosmological stru…
This article examines the foundation of the recently developed relativistic variational formalism[1]. Our work is heavily based on [2, 27] which extends this approach to the multi-fluid theory and examines its utility in astrophysics and…
The general relativistic non--linear dynamics of a self--gravitating collisionless fluid with vanishing vorticity is studied in synchronous and comoving -- i.e. {\em Lagrangian} -- coordinates. Writing the equations in terms of the metric…
Using thermodynamic relations and dimensional analysis we derive a general formula for the thermodynamical trace $2\mathcal{E}-DP$ for non-relativistic systems and $\mathcal{E-DP}$ for relativistic systems, where $D$ is the number of…
We study relativistic stars in the scale-dependent scenario, which is one of the approaches to quantum gravity, and where Newton's constant is promoted to a scale-dependent quantity. First, the generalized structure equations are derived…
We study a general relativistic particle action obtained by incorporating the Hamiltonian constraints into the formalism as a toy model for general relativity and string theory. We show how a non-vanishing cosmological constant and a…
Although general relativistic cosmological solutions, even in the presence of pressure, can be mimicked by using neo-Newtonian hydrodynamics, it is not clear whether there exists the same Newtonian correspondence for spherical static…
The explicit relationship is determined between the interior properties of a static cylindrical matter distribution and the metric of the exterior space-time according to Einstein gravity for space-time dimensionality larger or equal to…
I briefly present the foundations of relativistic cosmology, which are, General Relativity Theory and the Cosmological Principle. I discuss some relativistic models, namely, "Einstein static universe" and "Friedmann universes". The…
We present a general approach for the formulation of equations of motion for compact objects in general relativistic theories. The particle is assumed to be moving in a geometric background which in turn is asymptotically flat. Our approach…
In this first paper we present a Lagrangian framework for the description of structure formation in general relativity, restricting attention to irrotational dust matter. As an application we present a self-contained derivation of a…
We re-derive hydrodynamical equations in General Relativity (GR) in the comoving reference frame for spherical symmetry and obtain from them the well-known but not explicitly derived Lagrangean equations in Special Relativity (SR), that is,…
The Virial Theorem in the one- and two-dimensional spherical geometry are presented, in both classical and quantum mechanics. Choosing a special class of Hypervirial operators, the quantum Hypervirial relations in the spherical spaces are…
We provide a consistency relation between cosmological observables in general relativity without relying on the equation of state of dark energy. The consistency relation should be satisfied if general relativity is the correct theory of…
In this work we study the properties of rigidly rotating neutral dust solutions in general relativity. This class of solutions gained relevance recently due to applications to the dynamics of spiral galaxies. We show that this class could…
By following the spirit of arXiv:1003.5665, we define a new Tolman temperature of Kodama observer directly related to its acceleration. We give a generalized integral form of thermodynamics relation on virtual sphere of constant $r$ in…
A modification to the vis-viva equation that accounts for general relativistic effects is introduced to enhance the accuracy of predictions of orbital motion and precession. The updated equation reduces to the traditional vis-viva equation…
The kinetic approach to the formation of the filaments in the large-scale matter distribution in the Universe is considered within the Vlasov formalism. The structures arise due to the self-consistent dynamics, along with the repulsive term…
Equilibrium states in galactic dynamics can be described as stationary solutions of the Vlasov-Poisson system, which is the non-relativistic case, or of the Vlasov-Einstein system, which is the relativistic case. To obtain spherically…
The dispersion relation of de Sitter special relativity is obtained in a simple and compact form, which is formally similar to the dispersion relation of ordinary special relativity. It is manifestly invariant under change of scale of mass,…
We derive relativistic equations for charged and neutral spin particles. The approach for higher-spin particles is based on generalizations of the Bargmann-Wigner formalism. Next, we study, what new physical information can the introduction…