Related papers: Introduction to Regge Calculus for Gravitation
Einstein's General Relativity (GR) is possibly one of the greatest intellectual achievements ever conceived by the human mind. In fact, over the last century, GR has proven to be an extremely successful theory, with a well established…
Taking a hint from Dirac's large number hypothesis, we note the existence of cosmologically combined conservation laws that work to cosmologically long time. We thus modify Einstein's theory of general relativity with fixed gravitation…
After recalling the differential geometry of non-metric connections in the formalism of differential forms, we introduce the idea of a Non-Metricity (NM) connection, whose connection $1$--forms coincides with the non-metricity $1$--forms…
On the basis of an algebraic relation between torsion and a classical spinor field a new interpretation of Einstein-Cartan gravity interacting with classical spinor field is proposed. In this approach the spinor field becomes an auxiliary…
The recent classical nonlocal generalization of Einstein's theory of gravitation is presented within the framework of general relativity via the introduction of a preferred frame field. The nonlocal generalization of Einstein's field…
Cosmological observations indicate that the Einstein equation may not be entirely correct to describe gravity. However, numerous modifications of these equations usually do not affect foundations of the theory. In this paper two important…
The Einstein-Cartan-Kibble-Sciama ({\sf ECKS}) theory of gravity naturally extends Einstein\rq{}s general relativity ({\sf GR}) to include intrinsic angular momentum (spin) of matter. The main feature of this theory consists of an algebraic…
We construct differential geometry (connection, curvature, etc.) based on generalized derivations of an algebra ${\cal A}$. Such a derivation, introduced by Bresar in 1991, is given by a linear mapping $u: {\cal A} \rightarrow {\cal A}$…
One of the major developments of twentieth century physics has been the gradual recognition that a common feature of the known fundamental interactions is their gauge structure. In this article the authors review the early history of gauge…
We present a basics of the Einstein General Theory of Relativity. In the first part of this review we derive relations of Riemann geometry which are used in the General Relativity. In the second part we discuss Einstein Equations and some…
These Lecture notes give an introduction to Regge calculus as a discrete model of General Relativity.
A new principle in quantum gravity, dubbed spacetime complexity, states that gravitational physics emerges from spacetime seeking to optimize the computational cost of its quantum dynamics. Thus far, this principle has been realized at the…
Classical-particle trajectories are calculated for the static Einstein universe without requiring that the 3-space be closed and curved. Freely-moving test particles are found to return to their starting positions because of strong…
We introduce a modified Regge calculus for general relativity on a triangulated four dimensional Riemannian manifold where the fundamental variables are areas and a certain class of angles. These variables satisfy constraints which are…
In December 1911, Max Abraham published a paper on gravitation at the basis of which was Albert Einstein's 1911 June conclusion about a relationship between the velocity of light and the gravitational potential. In February 1912, Einstein…
The quantum field theoretic description of general relativity is a modern approach to gravity where gravitational force is carried by spin-2 gravitons. In the classical limit of this theory, general relativity as described by the Einstein…
This is a brief introduction to general relativity, designed for both students and teachers of the subject. While there are many excellent expositions of general relativity, few adequately explain the geometrical meaning of the basic…
In this paper, starting from the common foundation of Connes' noncommutative geometry (NCG) [1,2,3,4], various possible alternatives in the formulation of a theory of gravity in noncommutative spacetime are discussed in detail. The…
We give a short outline, in Sec.\ 2, of the historical development of the gauge idea as applied to internal ($U(1),\, SU(2),\dots$) and external ($R^4,\,SO(1,3),\dots$) symmetries and stress the fundamental importance of the corresponding…
In Einstein's general relativity, geometry replaces the concept of force in the description of the gravitation interaction. Such an approach rests on the universality of free-fall--the weak equivalence principle--and would break down…