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The strong proper time dilation and radial contraction in the gravitational field of compact sources leads to a frozen state of matter. It is shown that the falling particles and photons can not cross the gravitational radius due to the…
The cosmographic approach, which only relies upon the homogeneity and isotropy of the Universe on large scales, has become an essential tool in dealing with an increasing number of theoretical possibilities for explaining the late-time…
The gravitational field exterior respectively interior to a spherically symmetric, isolated body made of perfect fluid is examined within the quasi-metric framework (QMF). It is required that the gravitational field is "metrically static",…
We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the…
Rolling tachyon field models are among the candidates suggested as explanations for the recent acceleration of the Universe. In these models the field is expected to interact with gauge fields and lead to variations of the fine-structure…
As a sequel to (Berman, 2008a), we show that the rotation of the Universe can be dealt by generalised Gaussian metrics, defined in this paper. Robertson-Walker's metric has been employed with proper-time, in its standard applications; the…
(abridged) Gravitationally lensed quasars can be used as powerful cosmological and astrophysical probes. We can (i) infer the Hubble constant based on the time-delay technique, (ii) unveil substructures along the l.o.s. toward distant…
Context. High accuracy astrometric instruments like Gaia aiming at an accuracy of 1 microarcsecond cannot be considered as point-like observers in the framework of relativistic modelling of observable quantities. Aims. Special-relativistic…
General Relativity on closed spatial topologies can be derived, using a technique called "best-matching", as an evolving 3-geometry subject to constraints. These constraints can be thought of as a way of imposing temporal and spatial…
The Maxwell extension of the conformal algebra is presented. With the help of gauging the Maxwell-conformal group, a conformally invariant theory of gravity is constructed. In contrast to the conventional conformally invariant actions, our…
Einstein gravity coupled to a massive skew symmetric field F_{\mu\nu\lambda} leads to an acceleration law that modifies the Newtonian law of attraction between particles. We use a framework of non-perturbative renormalization group…
Based on the Generalized Principle of Inertia, which states that: \emph{An inanimate object moves freely, that is, with zero acceleration, in its own spacetime, whose geometry is determined by all of the forces affecting it,} we geometrize…
The origin of the Universe's late-time accelerated expansion remains unknown. The General Relativistic Entropic Acceleration (GREA) theory offers a compelling alternative to $\Lambda$CDM, attributing cosmic acceleration to entropy growth…
General relativity can be cast as a gauge theory by introducing a tetrad field and a spin-connection. This formalism was extended by replacing the tetrad field with a mixed tensor field independent of the metric tensor in order to develop a…
The debate on gravity theories to extend or modify General Relativity is very active today because of the issues related to ultra-violet and infra-red behavior of Einstein's theory. In the first case, we have to address the Quantum Gravity…
Problem of cosmological singularity of general relativity theory is discussed. The possible resolution of this problem in the framework of inflationary cosmology is proposed. Physical conditions leading to bouncing inflationary solutions in…
We use two model-independent methods to constrain the curvature of the universe. In the first method, we study the evolution of the curvature parameter ($\Omega_k^0$) with redshift by using the observations of the Hubble parameter and…
It is shown that under essentially all conditions, the non-linear classical equations governing gravitation and matter in cosmology have a solution in which far outside the horizon in a suitable gauge the reduced spatial metric (the spatial…
As a classical approach, the dynamics of the Universe, influenced by its dark components, are unveiled through prior modifications of Einstein's equations. Cosmography, on the other hand, is a highly efficient tool for reconstructing any…
In this article we outline the structure of a general relativistic astrometric model which has been developed to deduce the position and proper motion of stars from 1-microarcsecond optical observations made by an astrometric satellite…