Related papers: Moving Manifolds and General Relativity
We consider general relativity with cosmological constant minimally coupled to electromagnetic field and assume that four-dimensional space-time manifold is the warped product of two surfaces with Lorentzian and Euclidean signature metrics.…
We develop a novel approach to gravity that we call `matrix general relativity' (MGR) or `gravitational chromodynamics' (GCD or GQCD for quantum version). Gravity is described in this approach not by one Riemannian metric (i.e. a symmetric…
Gravity whose nature is fundamental to the understanding of solar system, galaxies and the structure and evolution of the Universe, is theorized by the assumption of curved spacetime, according to Einstein`s general theory of relativity…
We consider General Relativity (GR) on a space-time whose spatial slices are compact manifolds $M$ with non-empty boundary $\partial M$. We argue that this theory has a non-trivial space of `vacua', consisting of spatial metrics obtained by…
We provide a new extension of general relativity (GR) which has the remarkable property of being more constrained than GR plus a cosmological constant, having one less free parameter. This is implemented by allowing the cosmological…
We present a differential geometric formulation of the Poincare problem using the calculus of moving surfaces (CMS). In this framework, an n dimensional compact hypersurface evolves under a velocity field that couples motion to the…
Modified General Relativity (MGR) is the natural extension of General Relativity (GR). MGR explicitly uses the smooth regular line element vector field $(\bm{X},-\bm{X}) $, which exists in all Lorentzian spacetimes, to construct a…
The standard theory of General Relativity (GR) currently provides the most reliable description of all gravitational events in Astrophysics and Cosmology. However, current Astronomy allows measurements that contradict the predictions of GR…
The tree-level scattering amplitudes of general relativity encode the full non-linearity of the Einstein field equations. Yet remarkably compact expressions for these amplitudes have been found which seem unrelated to a perturbative…
Extensions of Einstein's General Relativity (GR) can formally be given a GR structure in which additional geometric degrees of freedom are mapped on an effective energy-momentum tensor. The corresponding effective cosmic medium can then be…
In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature…
We study general relativity in the framework of non-commutative differential geometry. In particular, we introduce a gravity action for a space-time which is the product of a four dimensional manifold by a two-point space. In the simplest…
The recent discovery of gravitational waves marks the culmination of a sequence of successful tests of the general theory of relativity (GR) since its formulation in 1915. Yet these tests remain confined to the scale of stellar systems or…
It is a review paper. General relativity (GR) is presented in the field theoretical form, where gravitational field (metric perturbations) together with other physical fields are propagated in an auxiliary arbitrary curved background…
We consider the fact that noticing on the operational meaning of the physical concepts played an impetus role in the appearance of general relativity (GR). Thus, we have paid more attention to the operational definition of the gravitational…
We show that General Relativity (GR) with cosmological constant may be formulated as a rather simple constrained SO(D-1,2) (or SO(D,1))-Yang-Mills (YM) theory. Furthermore, the spin connections of the Cartan-Einstein formulation for GR…
We discuss a set of relations, set in the form of results, conjectures and problems, between the L^{2}-norm of the Ricci curvature of a 3-manifold, the scalar curvature and the volume radius. We illustrate the scope of these relations with…
The standard paradigm of cosmology assumes General Relativity (GR) is a valid theory for gravity at scales in which it has not been properly tested. Developing novel tests of GR and its alternatives is crucial if we want to give strength to…
We consider general relativity with cosmological constant minimally coupled to the electromagnetic field and assume that the four-dimensional space-time manifold is a warped product of two surfaces with Lorentzian and Euclidean signature…
Three theoretical criteria for gravitational theories beyond general relativity are considered: obtaining the cosmological constant as an integration constant, deriving the energy conservation law as a consequence of the field equations,…