Related papers: Finsler geometric extension of Einstein gravity
We translate Penrose's singularity theorem to a Finsler spacetime. To that end, causal concepts in Lorentzian geometry are extended, including definitions and properties of focal points and trapped surfaces, with careful attention paid to…
Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a non degenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange…
We investigate gravitational lensing in the Palatini approach to the f(R) extended theories of gravity. Starting from an exact solution of the f(R) field equations, which corresponds to the Schwarzschild-de Sitter metric and, on the basis…
We study possible links between quantum gravity phenomenology encoding Lorentz violations as nonlinear dispersions, the Einstein-Finsler gravity models, EFG, and nonholonomic (non-integrable) deformations to Ho\v{r}ava-Lifshitz, HL, and/or…
We introduce a new class of $(\alpha,\beta)$-type exact solutions in Finsler gravity closely related to the well-known pp-waves in general relativity. Our class contains most of the exact solutions currently known in the literature as…
The Einstein theory of general relativity provides a peculiar example of classical field theory ruled by non-linear partial differential equations. A number of supplementary conditions (more frequently called gauge conditions) have also…
We investigate a possible unified theory of all interactions which is based only on fundamental spinor fields. The vielbein and metric arise as composite objects. The effective quantum gravitational theory can lead to a modification of…
We extend to the $n$-dimensional case a recent theorem establishing the validity of the Huygens' envelope principle for wavefronts in Finsler spaces. Our results have direct applications in analogue gravity models, for which the Fermat's…
Within the framework of projective geometry, we investigate kinematics and symmetry in $(\alpha,\beta)$ spacetime-one special types of Finsler spacetime. The projectively flat $(\alpha,\beta)$ spacetime with constant flag curvature is…
Finsler geometry is a natural and fundamental generalization of Riemann geometry. The Finsler structure depends on both coordinates and velocities. We present the arrival time delay of astroparticles subject to Lorentz violation in the…
f(Lovelock) gravities are simple generalizations of the usual f(R) and Lovelock theories in which the gravitational action depends on some arbitrary function of the corresponding dimensionally-extended Euler densities. In this paper we…
We study gravitational lensing by compact objects in gravity theories that can be written in a Post-Post-Newtonian (PPN) framework: i.e., the metric is static and spherically symmetric, and can be written as a Taylor series in m/r, where m…
Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are…
In the literature, there are several papers establishing a correspondence between a deformed kinematics and a nontrivial (momentum dependent) metric. In this work, we study in detail the relationship between the trajectories given by a…
Let $R$ be the $hh$-curvature associated with the Chern connection or the Cartan connection. Adopting the pulled-back tangent bundle approach to the Finslerian Geometry, an intrinsic characterization of $R$-Einstein metrics is given.…
We present a framework that reformulates gravitational lensing as an optical phenomenon governed by an effective refractive index, enabling exploration of modified gravity theories using undergraduate-level mathematics and optics. After…
The starting point of this work is the original Einstein action, sometimes called the Gamma squared action. Continuing from our previous results, we study various modified theories of gravity following the Palatini approach. The metric and…
A description of motion is proposed, adapted to the composite bundle interpretation of Poincar\'e Gauge Theory. Reference frames, relative positions and time evolution are characterized in gauge-theoretical terms. The approach is…
Using Fedosov theory of deformation quantization of endomorphism bundle we construct several models of pure geometric, deformed vacuum gravity, corresponding to arbitrary symplectic noncommutativity tensor. Deformations of Einstein-Hilbert…
A method to generalize results from Riemannian Geometry to Finsler geometry is presented. We use the method to generalize several results that involve only metric conditions. Between them we show that the topology induced by the Finsler…