Applying the cosmological principle to Finsler spacetimes, we identify the Lie Algebra of symmetry generators of spatially homogeneous and isotropic Finsler geometries, thus generalising Friedmann-Lemaître-Robertson-Walker geometry. In particul...
Physical foundations for relativistic spacetimes are revisited in order to check at what extent Finsler spacetimes lie in their framework. Arguments based on inertial observers (as in the foundations of special relativity and classical mechanics) are...
We investigate whether Szabo’s metrizability theorem can be extended to Finsler spaces of indefinite signature. For smooth, positive definite Finsler metrics, this important theorem states that, if the metric is of Berwald type (i.e., its Chern...
For the general class of pseudo-Finsler spaces with (α,β)-metrics, we establish necessary and sufficient conditions such that these admit a Finsler spacetime structure. This means that the fundamental tensor has a Lorentzian signature on a...
It is well-known that the universe is opaque to the propagation of Ultra-High-Energy Cosmic Rays (UHECRs) since these particles dissipate energy during their propagation interacting with the background fields present in the universe, mainly with the...
In this article, we study the form of the deviation of geodesics (tidal forces) and the Raychaudhuri equation in a Schwarzschild–Finsler–Randers (SFR) spacetime which has been investigated in previous papers. This model is obtained by con...
It is well-known that static vacuum solutions of Einstein equations are analytic in suitable coordinates. We ask here for an extension of this result in the context of Finsler gravity. We consider Finsler spacetimes that retain several properties of...
We revisit the physical arguments that led to the definition of the stress–energy tensor T in the Lorentz–Finsler setting (M,L) starting with classical relativity. Both the standard heuristic approach using fluids and the Lagrangian one a...
This article explores wormhole solutions within the framework of Finsler geometry and the modified gravity theory. Modifications in gravitational theories, such as f(R,T) gravity, propose alternatives that potentially avoid the exotic requirements. W...
The work presented in this paper aims to contribute to the problem of testing Finsler gravity theories by means of experiments and observations in the solar system. Within a class of spherically symmetric static Finsler spacetimes we consider a satel...
In this paper we present a survey of Fermat metrics and their applications to stationary spacetimes. A Fermat principle for light rays is stated in this class of spacetimes and we present a variational theory for the light rays and a description of t...
A six dimensional manifold of symmetric signature (3,3) is proposed as a space structure for building combined theory of gravity and electromagnetism. Special metric tensor is proposed, yielding the space which combines the properties of Riemann, Wey...
The class of warped product metrics can often be interpreted as key space models for the general theory of relativity and theory of space–time. In this paper, we study several non-Riemannian quantities in Finsler geometry. These non-Riemannian...
The class of warped product metrics can often be interpreted as key space models for the general theory of relativity and theory of space-time. In this paper, we first obtain the PDE characterization of Finsler warped product metrics with a vanishing...
By extending the four-dimensional semi-Riemann geometry to higher-dimensional Finsler/Hamilton geometry, the canonical quantization of the fundamental metric tensor of general relativity, i.e., an approach that tackles a geometric quantity, is derive...
We present a review of recent developments in cosmological models based on Finsler geometry, as well as geometric extensions of general relativity formulated within this framework. Finsler geometry generalizes Riemannian geometry by allowing the metr...
Whether an algebraic or a geometric or a phenomenological prescription is applied, the first fundamental form is unambiguously related to the modeling of the curved spacetime. Accordingly, we assume that the possible quantization of the first fundame...