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Einstein's celebrated theory of gravitation can be presented in three forms: general relativity, teleparallel gravity, and the rarely considered before symmetric teleparallel gravity. Extending the latter, we introduce a new class of…
The nature of gravity is fundamental to understand the scaffolding of the Universe and its evolution. Einstein's general theory of relativity has been scrutinized for over ninety five years and shown to describe accurately all phenomena…
The theory of gravity with a quadratic contribution of scalar curvature is investigated using a dynamical systems approach. The simplest Friedmann--Robertson--Walker metric is employed to formulate the dynamics in both the Jordan frame and…
As is well-known, Newton's gravitational theory can be formulated as a four-dimensional space-time theory and follows as singular limit from Einstein's theory, if the velocity of light tends to the infinity. Here 'singular' stands for the…
The analysis of measurements of accelerated observers in Minkowski spacetime has led to the development of nonlocal special relativity theory. Inertia and gravitation are intimately connected in accordance with the principle of equivalence.…
The renaissance of General Relativity witnessed considerable progress regarding both understanding and justifying Einstein's equations. Both general relativists and historians of the subject tend to share a view, General Relativity…
The description of gravity in the form of an embedding theory is based on the hypothesis that our space-time is a four-dimensional surface in a flat ten-dimensional space. The choice of standard Einstein-Hilbert action leads in this case to…
In this letter we will revise the steps followed by A. Einstein when he first wrote on cosmology from the point of view of the general theory of relativity. We will argue that his insightful line of thought leading to the introduction of…
Guided by the Einstein equivalence principle that identifies the phenomenon of gravitation as a manifestation of the dynamics of spacetime in contrast to a localizable force, we review and explore its consequences on formulating a theory of…
Flat space-time has not heretofore been thought a suitable locus in which to construct model universes because of the presumed necessity of incorporating gravitation in such models and because of the historical lack of a theory of…
Einstein's General theory of relativity permits spacetime singularities, where null geodesic congruences focus in the presence of matter, which satisfies an appropriate energy condition. In this paper, we provide a minimal defocusing…
A new classical theory of gravitation within the framework of general relativity is presented. It is based on a matrix formulation of four-dimensional Riemann-spaces and uses no artificial fields or adjustable parameters. The geometrical…
Padmanabhan [arXiv:1206.4916] argues that the cosmic acceleration can be understood from the perspective that spacetime dynamics is an emergence phenomena. By calculating the difference between the surface degrees of freedom and the bulk…
The extension of the so-called "empty" (with gravity and antigravity that compensate each other in full or do not exist at all) universe and cosmological redshift in it are considered in this paper. Its flat space-time can be submitted not…
In contrast to electrodynamics, Einstein's gravitation equations are not invariant with respect to a wide class of the mapping of field variables which leave equations of motion of test particles in a given coordinate system invariant. It…
We study the cosmological evolution of the field equations in the context of Einstein-Aether cosmology by including a scalar field in a spatially flat Friedmann--Lema\^{\i}tre--Robertson--Walker spacetime. Our analysis is separated into two…
When Einstein's equations for an asymptotically flat, vacuum spacetime are reexpressed in terms of an appropriate conformal metric that is regular at (future) null infinity, they develop apparently singular terms in the associated conformal…
The Conformal Einstein equations and the representation of spatial infinity as a cylinder introduced by Friedrich are used to analyse the behaviour of the gravitational field near null and spatial infinity for the development of data which…
Horava and Melby-Thompson recently proposed a new version of the Horava-Lifshitz theory of gravity, in which the spin-0 graviton is eliminated by introducing a Newtonian pre-potential $\phi$ and a local U(1) gauge field $A$. In this paper,…
We review the solution space for the field equations of Einstein's General Relativity for various static, spherically symmetric spacetimes. We consider the vacuum case, represented by the Schwarzschild black hole; the de…