Related papers: Geometric Unification in Classical Physics

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 study new classes of generic off-diagonal and diagonal cosmological solutions for effective Einstein equations in modified gravity theories, MGTs, with modified dispersion relations, MDRs, encoding possible violations of (local) Lorentz…

The Hubble constant proves to be the pseudo-Finsleroid--Landsberg factor. The covariantly conserved pseudo-Finsleroid--gravitational tensor is explicitly found after evaluating the respective Finsleroid--case curvature tensor and required…

Finsler geometry motivates a generalization of the Riemannian structure of spacetime to include dependence of the spacetime metric and associated invariant tensor fields on the four-velocity coordinates as well as the spacetime coordinates…

We study geometry and topology as complementary and dual aspects of the mathematical space. The same is used to get a better understanding of the Cosmological Constant. Having failed so far to include gravity in a proper unified framework…

Modern formulation of Finsler geometry of a manifold M utilizes the equivalence between this geometry and the Riemannian geometry of VTM, the vertical bundle over the tangent bundle of M, treating TM as the base space. We argue that this…

It is proposed how to impose a general type of ''noncommutativity'' within classical mechanics from first principles. Formulation is performed in completely alternative way, i.e. without any resort to fuzzy and/or star product philosophy,…

The study of arXiv:2502.01174 geometrization of classical fields in the 4d--Finsler space of MES (Model of Embedded Spaces) is continued. The model postulates a proper metric set of a distributed matter element and states that the…

Horndeski gravity is the most general scalar-tensor theory with one scalar field leading to second-order Euler-Lagrange field equations for the metric and scalar field, and it is based on Riemannian geometry. In this paper, we formulate an…

Finsler geometry is a natural generalization of pseudo-Riemannian geometry. It can be motivated e.g. by a modified version of the Ehlers-Pirani-Schild axiomatic approach to space-time theory. Also, some scenarios of quantum gravity suggest…

The Finsler spaces in which the tangent Riemannian spaces are conformally flat prove to be characterized by the condition that the indicatrix is a space of constant curvature. In such spaces the Finslerian normalized two-vector angle can be…

Starting with a field theoretic approach in Minkowski space, the gravitational energy momentum tensor is derived from the Einstein equations in a straightforward manner. This allows to present them as {\it acceleration tensor} = const.…

The geometric phase requires the multivaluedness of solutions to Fuchsian second-order equations. The angle, or its complement, is given by half the area of a spherical triangle in the case of three singular points, or half the area of a…

We analyse the Finsler geometries of the kinematic space of spinless and spinning electrically charged particles in an external Ra\~{n}ada field. We consider the most general actions that are invariant under the Lorentz, electromagnetic…

New classes of modified teleparallel theories of gravity are introduced. The action of this theory is constructed to be a function of the irreducible parts of torsion $f(T_{\rm ax},T_{\rm ten},T_{\rm vec})$, where $T_{\rm ax},T_{\rm ten}$…

Within the framework of the Finslerian approach to the problem of violation of Lorentz symmetry, consideration is given to a flat axially symmetric Finslerian space of events, which is the generalization of Minkowski space. Such an event…

The Finslerian unit ball is called the {\it Finsleroid} if the covering indicatrix is a space of constant curvature. We prove that Finsler spaces with such indicatrices possess the remarkable property that the tangent spaces are conformally…

We investigate the gravitational field of a kinetic gas beyond its usual derivation from the second moment of the one-particle distribution function (1PDF), that serves as energy-momentum tensor in the Einstein equations. This standard…

We investigate modified theories of gravity in the context of teleparallel geometries. It is well known that modified gravity models based on the torsion scalar are not invariant under local Lorentz transformations while modifications based…

The field equations of noncommutative gravity can be obtained by replacing all exterior products by twist-deformed exterior products in the action functional of general relativity, and are here studied by requiring that the torsion 2-form…