Related papers: Gravity from Noncommutative Geometry
The aim of the paper is to extend the notion of $\alpha$-geometry in the classical and in the noncommutative case by introducing a more general class of pull-back metrics and to give concrete formulas for the scalar curvature of these…
We prove the equivalence in the covariant phase space of the metric and connection formulations for Palatini gravity, with nonmetricity and torsion, on a spacetime manifold with boundary. To this end, we will rely on the cohomological…
We investigate static cylindrical solutions within an extended theory of modified gravity. By incorporating various coupling functions through a straightforward boost symmetry approach, we establish the equations of motion in a…
We show that the gravitational field equations derived from an action composed of i) an arbitrary function of the scalar curvature and other scalar fields plus ii) connection-independent kinetic and source terms, are identical whether one…
Explicit solutions to the conifold equations with complex dimension $n=3,4$ in terms of {\it{complex coordinates (fields)}} are employed to construct the Ricci-flat K\"{a}hler metrics on these manifolds. The K\"{a}hler 2-forms are found to…
The universal character of the gravitational interaction provided by the equivalence principle motivates a geometrical description of gravity. The standard formulation of General Relativity \`a la Einstein attributes gravity to the…
We consider $f\left(R\right) $-gravity in a Friedmann-Lema\^itre-Robertson-Walker spacetime with zero spatial curvature. We apply the Killing tensors of the minisuperspace in order to specify the functional form of $f\left(R\right) $ and…
We show how to define Riemannian metrics and connections on a noncommutative torus in such a way that an analogue of Levi-Civita's theorem on the existence and uniqueness of a Riemannian connection holds. The major novelty is that we need…
By using a projective connection over the space of two-dimensional affine connections, we are able to show that the metric interaction of Polyakov 2D gravity with a coadjoint element arises naturally through the projective Ricci tensor.…
We introduce a new definition of nonpositive curvature in metric spaces and study its relationship to the existing notions of nonpositive curvature in comparison geometry. The main feature of our definition is that it applies to all metric…
We first exhibit in the commutative case the simple algebraic relations between the algebra of functions on a manifold and its infinitesimal length element $ds$. Its unitary representations correspond to Riemannian metrics and Spin…
We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting historically from the Heisenberg relations, we will explain…
We study noncommutative Ricci flow in a finite dimensional representation of a noncommutative torus. It is shown that the flow exists and converges to the flat metric. We also consider the evolution of entropy and a definition of scalar…
We establish a new self-consistent system of equations for the gravitational and electromagnetic fields. The procedure is based on a non-minimal non-linear extension of the standard Einstein-Hilbert-Maxwell action. General properties of a…
In this paper we define an orientation of a measured Gromov-Hausdorff limit space of Riemannian manifolds with uniform Ricci bounds from below. This is the first observation of orientability for metric measure spaces. Our orientability has…
A connection-like objects, termed {\em hom-connections} are defined in the realm of non-commutative geometry. The definition is based on the use of homomorphisms rather than tensor products. It is shown that hom-connections arise naturally…
In this work a new non-minimally coupled model is presented, where a generic function $f(R)$ of the scalar curvature factors the usual Einstein-Hilbert action functional, motivated by relevant results obtained from similar models. Its…
We continue our systematic development of noncommutative and nonassociative differential geometry internal to the representation category of a quasitriangular quasi-Hopf algebra. We describe derivations, differential operators, differential…
This study explores the application of complexity factor within the context of Rastall gravity, exploring its implications on a static spacetime admitting spherical symmetry associated with anisotropic fluids under an electromagnetic field.…
On smooth manifolds of dimension $n \ge 4$, we prove that the torsion and curvature are, up to a scalar factor, the only pair of a vector-valued 2-form and an endomorphism-valued 2-form naturally associated with a linear connection that…