Related papers: Euclidean formulation of general relativity
In general relativity (GR), the metric tensor of spacetime is essential since it represents the gravitational potential. In other gauge theories (such as electromagnetism), the so-called premetric approach succeeds in separating the purely…
Three different representation of the proper Euclidean geometry are considered. They differ in the number of basic elements, from which the geometrical objects are constructed. In E-representation there are three basic elements (point,…
We show how to formulate physical theory taking as a starting point the set of states (geometric approach). We discuss the relation of this formulation to the conventional approach to classical and quantum mechanics and the theory of…
Fefferman and Graham showed some time ago that four dimensional conformal geometries could be analyzed in terms of six dimensional, ambient, Riemannian geometries admitting a closed homothety. Recently it was shown how conformal geometry…
In order to explain weak gravitation in our 4-dimensional universe, a 6-dimensional model with a small extra 2D sphere is proposed. The traceless energy-momentum tensor is quite naturally appeared in our 6-dimensional model. The warp factor…
Assuming that the relativistic universe is homogeneous and isotropic, we can unambiguously determine its model and physical properties, which correspond with the Einstein general theory of relativity (and with its two special partial…
The gravitation equations of the general relativity, written for Riemannian space-time geometry, are extended to the case of arbitrary (non-Riemannian) space-time geometry. The obtained equations are written in terms of the world function…
A pedagogical description of a simple ungeometrical approach to General Relativity is given, which follows the pattern of well understood field theories, such as electrodynamics. This leads quickly to most of the important weak field…
The Palatini formalism is developed for gravitational theories in flat geometries. We focus on two particularly interesting scenarios. First, we fix the connection to be metric compatible, but we follow a completely covariant approach by…
We show that the general theory of relativity can be formulated in the language of Weyl geometry. We develop the concept of Weyl frames and point out that the new mathematical formalism may lead to different pictures of the same…
We analyze both the feasibility and reasonableness of a classical Euclidean Theory of Everything (TOE), which we understand as a TOE based on an Euclidean space and an absolute time over which deterministic models of particles and forces…
In 1945 Einstein concluded that [1]: 'The present theory of relativity is based on a division of physical reality into a metric field (gravitation) on the one hand, and into an electromagnetic field and matter on the other hand. In reality…
Random tensor models can be used as combinatorial devices to generate Euclidean dynamical triangulations. A physical continuum limit of dynamical triangulations requires a suitable generalization of the double-scaling limit of random…
The Standard Model of particle physics describes electromagnetic, weak, and strong interactions, which are three of the four known fundamental forces of nature. The unification of the fourth interaction, gravity, with the Standard Model has…
General Relativity extended through a dynamical scalar quartet is proposed as a theory of the scalar-vector-tensor gravity, generically describing the unified gravitational dark matter (DM) and dark energy (DE). The implementation in the…
Light is the richest information retriever for most physical systems, particularly so for astronomy and cosmology, in which gravitation is of paramount importance, and also for solid state defects and metamaterials, in which some effects…
Three variational vector equations are derived for the extended particle-field object located on the light cone. Point sources are excluded from the pure field equations and all physical magnitudes are free from divergences. Accepting 3D…
Within the framework of geodetic brane gravity, the Universe is described as a 4-dimensional extended object evolving geodetically in a higher dimensional flat background. In this paper, by introducing a new pair of canonical fields…
When constructing general relativity (GR), Einstein required 4D general covariance. In contrast, we derive GR (in the compact, without boundary case) as a theory of evolving 3-dimensional conformal Riemannian geometries obtained by imposing…
The method of four-dimensional Causal Dynamical Triangulations provides a background-independent definition of the sum over geometries in quantum gravity, in the presence of a positive cosmological constant. We present the evidence…