Related papers: Causal structure and electrodynamics on Finsler sp…
We investigate the causal structure of two-sheeted space-times using the tools of Lorentzian spectral triples. We show that the noncommutative geometry of these spaces allows for causal relations between the two sheets. The computation is…
We discuss a variational approach to the length functional and its relation to sub-Hamiltonian equations on sub-Finsler manifolds. Then, we introduce the notion of the nonholonomic sub-Finslerian structure and prove that the distributions…
A classical result in Lorentzian geometry states that a strongly causal spacetime is globally hyperbolic if and only if the Lorentzian distance is finite valued for every metric choice in the conformal class. It is proven here that a…
We recast the tools of ``global causal analysis'' in accord with an approach to the subject animated by two distinctive features: a thoroughgoing reliance on order-theoretic concepts, and a utilization of the Vietoris topology for the space…
This article is an exposition of four loosely related remarks on the geometry of Finsler manifolds with constant positive flag curvature. <p> The first remark is that there is a canonical Kahler structure on the space of geodesics of such a…
No Hopf-Rinow Theorem is possible in Lorentzian Geometry. Nonetheless, we prove that a spacetime is globally hyperbolic if and only if it is metrically complete with respect to the null distance of a time function. Our approach is based on…
In this paper we first study some global properties of the energy functional on a non-reversible Finsler manifold. In particular we present a fully detailed proof of the Palais--Smale condition under the completeness of the Finsler metric.…
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…
In this paper we formulate the relationship between force-free electrodynamics and foliations. The background metric, is considered predetermined and electrically neutral, but otherwise arbitrary. As it turns out, solutions to force-free…
Lightlike Cartan geometries are introduced as Cartan geometries modelled on the future lightlike cone in Lorentz-Minkowski spacetime. Then, we provide an approach to the study of lightlike manifolds from this point of view. It is stated…
We describe the geometry of geodesics on a Lorentz ellipsoid: give explicit formulas for the first integrals (pseudo-confocal coordinates), curvature, geodesically equivalent Riemannian metric, the invariant area-forms on the time- and…
The motion of particles on spherical $1 + 3$ dimensional spacetimes can, under some assumptions, be described by the curves on a 2-dimensional manifold, the optical and Jacobi manifolds for null and timelike curves, respectively. In this…
Spacetime is represented by ordered sequences of topologically closed Poincare sections of the primary space constructed of primary empty cells. These mappings are constrained to provide homeomorphic structures serving as frames of…
It is reasonably well-known that birefringent crystal optics can to some extent be described by the use of pseudo-Finslerian spacetimes (an extension of pseudo-Riemannian spacetime). What is less commonly appreciated is that there are two…
Recently, a link between Lorentzian and Finslerian Geometries has been carried out, leading to the notion of wind Riemannian structure (WRS), a generalization of Finslerian Randers metrics. Here, we further develop this notion and its…
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…
In this talk a previous theorem on geodesic completeness of diagonal cylindrical spacetimes will be generalized to cope with the nondiagonal case. A sufficient condition for such spacetimes to be causally geodesically complete will be given
A number of techniques in Lorentzian geometry, such as those used in the proofs of singularity theorems, depend on certain smooth coverings retaining interesting global geometric properties, including causal ones. In this note we give…
While the postulate of covariance of Maxwell's equations for all inertial observers led Einstein to special relativity, it was the further demand of general covariance -- form invariance under general coordinate transformations, including…
Within the synthetic-geometric framework of Lorentzian (pre-)length spaces developed in Kunzinger and S\"amann (Ann. Glob. Anal. Geom. 54(3):399--447, 2018) we introduce a notion of a hyperbolic angle, an angle between timelike curves and…