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In this paper, we consider spatially homogenous and anisotropic Bianchi type I universe in the context of F(T) gravity. We construct some corresponding models using conservation equation and equation of state parameter representing…
For the strong gravitational wave model, an explicit transformation is obtained from a privileged coordinate system with a wave variable to a synchronous reference frame with separation of time and space variables. In a synchronous…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
The qualitative properties of spatially homogeneous stiff perfect fluid and minimally coupled massless scalar field models within general relativity are discussed. Consequently, by exploiting the formal equivalence under conformal…
The Klein-Gordon equations were recently solved in general relativity for the case of a plane-symmetric static massless scalar field with cosmological constant. By analytic continuation, time-dependent solutions can be obtained that…
In the present investigation compact stellar models are dealt with in the framework of the modified gravity theory, specifically of $f(\mathbb{T},\mathcal{T})$ type. We have considered that the compact objects are following a spherically…
The evolution of inhomogeneities in a spherical collapse model is studied by expanding the Einstein equation in powers of inverse radial parameter. In the linear regime, the density contrast is obtained for flat, closed and open universes.…
The general world model for homogeneous and isotropic universe has been roposed. For this purpose, we introduce a global and fiducial system of reference (world reference frame) constructed on a 5-dimensional space-time that is embedding…
We consider the possibility of describing the Higgs effect in unified theories without the Higgs potential in the presence of the Einstein gravity with the conformal gravity-scalar coupling under the assumption of homogeneous matter…
A class of $ G $-invariant Einstein-Yang-Mills (EYM) systems with cosmological constant on homogeneous spaces $ G / H $, where $ G $ is a semisimple compact Lie group, is presented. These EYM--systems can be obtained in terms of dimensional…
In this paper we consider the single patch pseudo-spectral scheme for tensorial and spinorial evolution problems on the 2-sphere presented in [3,4] which is based on the spin-weighted spherical harmonics transform. We apply and extend this…
In this paper, we study spatially homogeneous solutions of the Boltzmann equation in special relativity and in Robertson-Walker spacetimes. We obtain an analogue of the Povzner inequality in the relativistic case and use it to prove global…
4-dimensional homogeneous isotropic cosmological models obtained from solutions of vacuum 5-dimensional Einstein equations are considered. It is assumed, that the G(55)-component of the 5-d metric simulates matter in the comoving frame of…
Einstein's field equations with cosmological constant are analysed for a static, spherically symmetric perfect fluid having constant density. Five new global solutions are described. One of these solutions has the Nariai solution joined on…
The existence of stationary solutions to the Einstein-Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat…
New classes of classically integrable models in the cosmological theories with a scalar field are obtained by using freedoms of defining time and fields. In particular, some models with the sum of exponential potentials in the flat spatial…
The semi-classical approach to the quantum geometrodynamical model is used for the description of the properties of the universe on extremely small spacetime scales. Quantum theory for a homogeneous, isotropic and closed universe is…
A new approach to tackle Einstein equations for an isotropic and homogeneous Friedmann--Robertson--Walker Universe in the presence of a quintessence scalar field is devised. It provides a way to get a simple exact solution to these…
The general stationary cylindrically symmetric solution of Einstein-massless scalar field system with a non-positive cosmological constant is presented. It is shown that the general solution is characterized by four integration constants.…
The classification of equilibria for the spatially homogeneous Boltzmann equation for Fermi-Dirac particles is proved for any $n$-dimensional velocity space with $n\ge 2$. The same classification has been proven in \cite{Lu2001} for $n=3$.…