Related papers: On the nonsymmetric purely affine gravity
We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The…
We use curvature decompositions to construct generating sets for the space of algebraic curvature tensors and for the space of tensors with the same symmetries as those of a torsion free, Ricci symmetric connection; the latter naturally…
Within the framework of metric-affine gravity (MAG, metric and an independent linear connection constitute spacetime), we find, for a specific gravitational Lagrangian and by using {\it prolongation} techniques, a stationary axially…
A Lagrangian depending on geometric variables (metric, affine connection, gauge group generators) is given which maintains compatibility with General Relativity. It generates the dynamics for Electromagnetism and other Gauge Fields along…
We consider a class of metric-affine gravitational theories with action quadratic in curvature and torsion tensors. Using the heat kernel technique, we compute the torsion contributions to the one-loop counterterms in the ultraviolet limit.…
Determinants of the second-rank tensors stand useful in forming generally invariant terms as in the case of the volume element of the gravitational actions. Here, we extend the action of the matter fields by an arbitrary function $f(D)$ of…
f(R)-gravity with geometric torsion (not related to any spin fluid) is considered in a cosmological context. We derive the field equations in vacuum and in presence of perfect-fluid matter and discuss the related cosmological models.…
We explore the role of the affine connection in $f(Q)$ gravity, a modified theory where gravity is governed by non-metricity within the symmetric teleparallel framework. Although the connection is constrained to be flat and torsionless, it…
We suggest an extension of the Yang-Mills theory which includes non-Abelian tensor gauge fields. The invariant Lagrangian is quadratic in the field strength tensors and describes interaction of charged tensor gauge bosons of arbitrary large…
Quasi-topological terms in gravity can be viewed as those that give no contribution to the equations of motion for a special subclass of metric ans\"atze. They therefore play no r\^ole in constructing these solutions, but can affect the…
The infinitesimal transformations that leave invariant a two-covariant symmetric tensor are studied. The interest of these symmetry transformations lays in the fact that this class of tensors includes the energy-momentum and Ricci tensors.…
We consider the sum of the Einstein-Hilbert action and a Pontryagin density (PD) in arbitrary even dimension $D$. All curvatures are functions of independent affine (torsionless) connections only. In arbitrary dimension, not only in $D=4n$,…
The general relativistic non--linear dynamics of a self--gravitating collisionless fluid with vanishing vorticity is studied in synchronous and comoving -- i.e. {\em Lagrangian} -- coordinates. Writing the equations in terms of the metric…
We consider antisymmetric Metric-Affine Theories of Gravity with a Lagrangian containing the most general terms up to dimension four and search for theories that are ghost- and tachyon-free when expanded around flat space. We find new…
We show that it is possible to go beyond the simple kinematical aspects of the analog models of gravity. We exhibit the form of the Lagrangian that describes the dynamics of a self-interacting field $ \phi $ as an interaction between $ \phi…
Manifolds endowed with torsion and nonmetricity are interesting both from the physical and the mathematical points of view. In this paper, we generalize some results presented in the literature. We study Einstein manifolds (i.e., manifolds…
We study properties of Newton-Cartan gravity under transformations into all noninertial, nonrelativistic reference frames. The set of these transformations has the structure of an infinite dimensional Lie group, called the Galilean line…
Divergence-free symmetric tensors seem ubiquitous in Mathematical Physics. We show that this structure occurs in models that are described by the so-called "second" variational principle, where the argument of the Lagrangian is a closed…
We study $f(R,T)$ gravity, in which the curvature $R$ appearing in the gravitational Lagrangian is replaced by an arbitrary function of the curvature and the trace $T$ of the stress-energy tensor. We focus primarily on situations where $f$…
We analyze the properties of foliations in presence of non-metricity, deriving the generalized Gauss-Codazzi relations in full generality. These results are employed to study the teleparallel framework of non-metric geometry, obtaining…