Related papers: Differential geometry, Palatini gravity and reduct…
Some mathematical aspects of using the translation group as an internal symmetry group in a gauge field theory are presented and discussed. The traditional manner in which gravitation can be accounted for by the introduction of a global…
Two approaches to the study of cosmological density perturbations in modified theories of Palatini gravity have recently been discussed. These utilise, respectively, a generalisation of Birkhoff's theorem and a direct linearization of the…
In its canonical formulation, general relativity is subject to gauge transformations that are equivalent to space-time coordinate changes of general covariance only when the gauge generators, given by the Hamiltonian and diffeomorphism…
It has been suggested that the recent acceleration of the expansion of the Universe is due a modified gravitational action consisting of the Einstein-Hilbert term plus a term proportional to the reciprocal of the Ricci scalar. Although the…
In this paper we show that a variational reduction procedure can be defined for Lagrangian systems subject to scaling symmetries (i.e. Lagrangian systems defined by a homogenous Lagrangian function), in such a way that the trajectories of…
We study the field equations of modified theories of gravity in which the lagrangian is a general function of the Ricci scalar and Ricci-squared terms in Palatini formalism. We show that the independent connection can be expressed as the…
In the literature, there are several papers establishing a correspondence between a deformed kinematics and a nontrivial (momentum dependent) metric. In this work, we study in detail the relationship between the trajectories given by a…
Generalized differential forms are used in discussions of metric geometries and Einstein's vacuum field equations. Cartan's structure equations are generalized and applied. In particular flat generalized connections are associated with any…
We work on the Lagrangian and the Hamiltonian formulations of the Palatini action. In the Lagrangian formulation, we find that we need to assume the metric compatibility and the torsion zero or to assume the tetrad compatibility to describe…
The starting point of this work is the original Einstein action, sometimes called the Gamma squared action. Continuing from our previous results, we study various modified theories of gravity following the Palatini approach. The metric and…
A generalized definition of a frame of reference in spaces with affine connections and metrics is proposed based on the set of the following differential-geometric objects: (a) a non-null (non-isotropic) vector field, (b) the orthogonal to…
We study the most general solution for affine connections that are compatible with the variational principle in the Palatini formalism for the Einstein-Hilbert action (with possible minimally coupled matter terms). We find that there is a…
We present the invariant structure of a Holomorphic Unified Field Theory in which gravity and gauge interactions arise from a single geometric framework. The theory is formulated using a product principal bundle, with one connection, and…
The new approach to quantize the gravity based on the notion of differential algebra is suggested. It is shown that the differential geometry of this object can not be described in terms of points. The spatialization procedure giving rise…
The existing approaches to quantization of gravity aim at giving quantum description of 3-geometry following to the ideas of the Wheeler -- DeWitt geometrodynamics. In this description the role of gauge gravitational degrees of freedom is…
We establish a Lagrangian variational framework for general relativistic continuum theories that permits the development of the process of Lagrangian reduction by symmetry in the relativistic context. Starting with a continuum version of…
In a previous paper we showed that static spherically symmetric objects which, in the vicinity of their surface, are well-described by a polytropic equation of state with 3/2<Gamma<2 exhibit a curvature singularity in Palatini f(R) gravity.…
Following the approach of Grignani and Nardelli [1], we show how to cast the two-dimensional model $L \sim curv^2 + torsion^2 + cosm.const$ -- and in fact any theory of gravity -- into the form of a Poincare gauge theory. By means of the…
The framework of the Covariant Canonical Gauge theory of Gravity (CCGG) is described in detail. CCGG emerges naturally in the Palatini formulation, where the vierbein and the spin connection are independent fields. Neither torsion nor…
The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor…