Related papers: Geometry of teleparallel theories
In this paper we discuss on the phenomenological viability of nonmetricity theories of gravity which are based in the class of generalized Weyl spacetimes -- denoted by $W_4$ -- where arbitrary nonmetricity is allowed. This class of…
The notion of spacetime symmetry is essential to describe gravitating physical systems like planets, stars, black holes, or the universe as a whole, since they possess, at least to good approximation, spherical, axial, or spatially…
It is shown that the geometry of parallelizable manifolds can be extended to non-parallelizable ones by extending the connection that a global frame field would define on a parallelizable manifold to a connection that a singular frame field…
After reminder some facts concerning general relativity ({\bf GR}) we pass to teleparallel gravity. We are confining the special model of the teleparallel gravity, which is popular recently, called {\it the teleparallel equivalent of…
Teleparallel Gravity is a gauge theory where gravity is a manifestation of the torsion of space-time and its success relies on being a possible solution to some problems of General Relativity. In this essay we introduce the construction of…
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…
The geometry of parallelizable manifolds is presented from the standpoint of regarding it as conventional (e.g., Euclidian or Minkowskian) geometry, when it is described with respect to an anholonomic frame field that is defined on the…
When joined the unified gauge picture of fundamental interactions, the gravitation theory leads to geometry of a space-time which is far from simplicity of pseudo-Riemannian geometry of Einstein's General Relativity. This is geometry of the…
We derive the Hamiltonian function for extended teleparallel theories of gravity in their covariant formulation. In particular, we present the Hamiltonian for $f(T)$ gravity and New General Relativity. From this, we obtain the related…
An alternative interpretation of the conformal transformations of the metric is discussed according to which the latter can be viewed as a mapping among Riemannian and Weyl-integrable spaces. A novel aspect of the conformal transformation's…
General Relativity and its higher derivative extensions have symmetric teleparallel reformulations in terms of the non-metricity tensor within a torsion-free and flat geometry. These notes present a derivation of the exact propagator for…
We construct a symmetric teleparallel gravity model which is non-minimally coupled with electromagnetic field in four dimensions inspired by its Riemannian equivalent. We derive the field equations by taking the variation of this model,…
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…
In this paper, it is argued that in gravity theories the local Lorentz group can not be considered as a gauge group in the sense of Yang-Mills theories, the Lorentz connection is not a gauge potential but an artificial force, the inertial…
As true as it is that a bricklayer needs a plumb line and a T-square, so it is that a physicist using general relativity needs how to draw geodesics and use fields of congruent vector frames of reference. While the first part of the…
Recently it has been argued that autoparallels should be the correct description of free particle motion in spaces with torsion, and that such trajectories can be derived from variational principles if these are suitably adapted. The…
In theories such as teleparallel gravity and its extensions, the frame basis replaces the metric tensor as the primary object of study. A choice of coordinate system, frame basis and spin-connection must be made to obtain a solution from…
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…
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…
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…