Finsler Gravity Theories Research Articles

Numerical Modelling of Satellite Downlink Signals in a Finslerian-Perturbed Schwarzschild Spacetime

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 satellite with an on-board atomic clock, orbiting in the Finslerian-perturbed gravitational field of the earth, whose time signal is transmitted to a ground station, where its receive time and frequency are measured with respect to another atomic clock. This configuration is realized by the Galileo 5 and 6 satellites that have gone astray and are now on non-circular orbits. Our method consists in the numerical integration of the satellite’s orbit, followed by an iterative procedure which provides the numerically integrated signals, i.e., null geodesics, from the satellite to the ground station. One of our main findings is that for orbits that are considerably more eccentric than the Galileo 5 and 6 satellite orbits, Finslerian effects can be separated from effects of perturbations of the Schwarzschild spacetime within the Lorentzian geometry. We also discuss the separation from effects of non-gravitational perturbations. This leads us to the conclusion that observations of this kind combined with appropriate numerical modelling can provide suitable tests of Finslerian modifications of general relativity.

A divergence theorem for pseudo-Finsler spaces

We study the divergence theorem on pseudo-Finsler spaces and obtain a completely Finslerian version for spaces having a vanishing mean Cartan torsion. This result helps to clarify the problem of energy-momentum conservation in Finsler gravity theories.

PRINCIPLES OF EINSTEIN–FINSLER GRAVITY AND PERSPECTIVES IN MODERN COSMOLOGY

We study the geometric and physical foundations of Finsler gravity theories with metric compatible connections defined on tangent bundles, or (pseudo) Riemannian manifolds, endowed with nonholonomic frame structure. Several generalizations and alternatives to Einstein gravity are considered, including modifications with broken local Lorentz invariance. It is also shown how such theories (and general relativity) can be equivalently re-formulated in Finsler like variables. We focus on prospects in modern cosmology and Finsler acceleration of Universe. Einstein–Finsler gravity theories are elaborated following almost the same principles as in the general relativity theory but extended to Finsler metrics and connections. Finally, some examples of generic off-diagonal metrics and generalized connections, defining anisotropic cosmological Einstein–Finsler spaces are analyzed; certain criteria for the Finsler accelerating evolution are formulated.

Principles of Einstein-Finsler Gravity and Cosmology

We analyze the foundations of Finsler gravity theories with metric compatible connections constructed on nonholonomic tangent bundles, or (pseudo) Riemannian manifolds. There are considered "minimal" modifications of Einstein gravity (including theories with violation of local Lorentz invariance) and shown how the general relativity theory and generalizations can be equivalently re-formulated in Finsler like variables. We focus on Finsler branes solutions and perspectives in modern cosmology.