相关论文: Pseudo-Finsleroid metric function of spatially ani…
The pseudo-Finsleroid relativistic metric was constructed upon assuming that the involved vector field $b_i$ is time-like. In the present paper it is shown that the metric admits just the alternative counterpart in which the field is…
When a single time-like vector is distinguished geometrically to present the only preferred direction in extending the pseudoeuclidean geometry, the hyperboloid may not be regarded as an exact carrier of the unit-vector image. So under…
We undertake to show how the relativistic Finslerian Metric Function (FMF) should arise under uni-directional violation of spatial isotropy, keeping the condition that the indicatrix (mass-shell) is a space of constant negative curvature.…
The work focuses upon the relativistic and geometric properties of the space--time endowed tentatively with the metric function of the Berwald--Moor type. The zero curvature of indicatrix is a remarkable property of the approach. We…
A particular Finsler-metric proposed in [1,2] and describing a geometry with a preferred null direction is characterized here as belonging to a subclass contained in a larger class of Finsler-metrics with one or more preferred directions…
Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of…
Upon straightforward four--directional extension of the special--relativistic two--dimensional transformations to the four--dimensional case we lead to convenient totally anisotropic kinematic transformations, which prove to reveal many…
A systematic approach has been developed to encompass the Minkowski-type extension of Euclidean geometry such that a one-vector anisotropy is permitted, retaining simultaneously the concept of angle. For the respective geometry, the…
The Finslerian extension of the Euclidean metric is proposed and studied under rigorous conditions that the associated indicatrix is regular and convex. The relativistic pseudo-Euclidean metric is extended, too. The extensions show distinct…
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…
The method of simple straightforward calculation of the curvature tensor of the Finsleroid--regular space is indicated. The Schwarzschild metric which underlines the gravitational field produced by static spherical-symmetric body is shown…
Recent links between Finsler Geometry and the geometry of spacetimes are briefly revisited, and prospective ideas and results are explained. Special attention is paid to geometric problems with a direct motivation in Relativity and other…
Finsler geometry naturally appears in the description of various physical systems. In this review I divide the emergence of Finsler geometry in physics into three categories: as dual description of dispersion relations, as most general…
It is shown that the problem of a possible violation of the Lorentz transformations at Lorentz factors $\gamma >5\times 10^{10} ,$ indicated by the situation which has developed in the physics of ultra-high energy cosmic rays (the absence…
Finslerian extension of the theory of relativity implies that space-time can be not only in an amorphous state which is described by Riemann geometry but also in ordered, i.e. crystalline states which are described by Finsler geometry.…
The Finslerian post-Lorentzian kinematic transformations can explicitly be obtained under uni-directional breakdown of spatial isotropy, provided that the requirement that the relativistic unit hypersurface (indicatrix or mass shell) be a…
We briefly review some basic concepts of parallel displacement in Finsler geometry. In general relativity, the parallel translation of objects along the congruence of the fundamental observer corresponds to the evolution in time. By…
We provide a Finslerian extension of the Schwarzschild metric based on heuristic arguments. The proposed metric asymptotically approaches not the Minkowski space-time but the Bogoslovsky locally anisotropic space-time which arises naturally…
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…
For well-defined Finsleroid-relativistic space $\cE_g^{SR}$ (with the upperscript SR meaning Special-Relativistic) due only to accounting a characteristic parameter $g$ which measures the deviation of the geometry from its pseudoeuclidean…