相关论文: Equivalence between an extension of teleparallelis…

We present the general theory of relativity in the language of a non-Riemannian geometry, namely, Weyl geometry. We show that the new mathematical formalism may lead to different pictures of the same gravitational phenomena, by making use…

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…

This paper presents three aspects by which the Weyl geometric generalization of Riemannian geometry, and of Einstein gravity, sheds light on actual questions of physics and its philosophical reflection. After introducing the theory's…

One of the important extensions of Riemann geometry is Weyl geometry, which is essentially based on the ideas of conformal invariance and nonmetricity. A similar non-Riemannian geometry was proposed by Erwin Schr\"{o}dinger in the late…

There is a growing interest in modified gravity theories based on torsion, as these theories exhibit interesting cosmological implications. In this work, inspired by the teleparallel formulation of general relativity, we present its…

We first present an overview of the Schwarzschild vacuum spacetime within general relativity, with particular emphasis on the role of scalar polynomial invariants and the null frame approach (and the related Cartan invariants), that…

General relativity can be presented in terms of other geometries besides Riemannian. In particular, teleparallel geometry (i.e., curvature vanishes) has some advantages, especially concerning energy-momentum localization and its…

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…

The teleparallel formulation of gravity theories reveals close structural analogies to electrodynamics, which are more hidden in their usual formulation in terms of the curvature of spacetime. We show how every locally Lorentz invariant…

We develop the properties of Weyl geometry, beginning with a review of the conformal properties of Riemannian spacetimes. Decomposition of the Riemann curvature into trace and traceless parts allows an easy proof that the Weyl curvature…

Teleparallel gravity has significantly increased in popularity in recent decades, bringing attention to Einstein's other theory of gravity. In this Review, we relate this form of geometry to the broader metric-affine approach to forming…

A review of the teleparallel equivalent of general relativity is presented. It is emphasized that general relativity may be formulated in terms of the tetrad fields and of the torsion tensor, and that this geometrical formulation leads to…

Riemannian and teleparallel geometrical approaches to the investigation of Maxwell electrodynamics shown that a unified field theory of gravitation and electromagnetism a la Einstein can be obtained from a stationary metric. This idea…

We derive a Weyl invariant equation for Gravity by gauging the global Weyl invariance of vacuum Einstein equations. The equation is linear in the curvature and a natural generalization of Einstein equations to Weyl geometry. The system has…

In this paper, we construct a field theory unifying gravity and electromagnetism in the context of Extended Absolute Parallelism (EAP-) geometry. This geometry combines, within its structure, the geometric richness of the tangent bundle and…

Just after Weyl's paper (Weyl in Gravitation und Elektrizit\"at, Sitzungsber. Preuss. Akad., Berlin, 1918) Einstein claimed that a gravity model written in a spacetime geometry with non-metricity suffers from a phenomenon, the so-called…

We extend our program, of coupling theories to scale in order to make their Weyl invariance manifest, to include interacting theories, fermions and supersymmetric theories. The results produce mass terms coinciding with the standard ones…

In this Letter we consider a general quadratic parity-preserving theory for a general flat connection. Imposing a local symmetry under the general linear group singles out the general teleparallel equivalent of General Relativity carrying…

In this work a tetrad theory of gravity, invariant under conformal transformations, is investigated. The action of the theory is similar to the action of Maxwell's electromagnetism. The role of the electromagnetic gauge potential is played…

We introduce the new algebraic property of Weyl compatibility for symmetric tensors and vectors. It is strictly related to Riemann compatibility, which generalizes the Codazzi condition while preserving much of its geometric implications.…