Related papers: Rigidity and Parallelism in the spacetime
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…
The debate on the physical relevance of conformal transformations can be faced by taking the Palatini approach into account to gravitational theories. We show that conformal transformations are not only a mathematical tool to disentangle…
We describe space--time fluctuations by means of small fluctuations of the metric on a given background metric. From a minimally coupled Klein--Gordon equation we obtain within a weak-field approximation up to second order and an averaging…
We consider an inverse variational problem for the lines of constant curvature in (pseudo-)Euclidean two-, three-, and four-dimensional spaces. The accumulated results are physically meaningful in the case of relativistic mechanics of…
We investigate the impact of singularities occurring at future times in solutions of the Friedmann equations expressed in conformal coordinates. We focus on the consequences of extending the time coordinate through the singularity for the…
We discuss how the finiteness and universality of the speed of light arise in the theoretical framework introduced in [1], and derive generalized coordinate transformations, that allow to investigate physical systems in a non-classical…
Causal rigid particles whose action includes an {\it arbitrary} dependence on the world-line extrinsic curvature are considered. General classes of solutions are constructed, including {\it causal tachyonic} ones. The Hamiltonian…
This contribution shows that the main topics of Relativity can be discussed at an elementary level and in a considerable extent - including the formal results of "Time Dilation" and "Lorentz Contraction" - by a minor modification of the…
We investigate how deformations of special relativity in momentum space can be extended to position space in a consistent way, such that the dimensionless contraction between wave-vector and coordinate-vector remains invariant. By using a…
While adhering to the formalism of Special and General Relativity, this paper considers the interpretation of clock rates and the rating of clocks in detail. We also pay particular attention to the crucial requirement of reciprocity between…
In this extended note a critical discussion of an extension of the Lorentz transformations for velocities faster than the speed of light given recently by Hill and Cox is provided. The presented approach reveals the connection between…
Translational invariance requires that physical predictions are independent of the choice of spatial coordinate system used. The time dilatation effect of special relativity is shown to manifestly respect this invariance. Consideration of…
To consider a medium carrying light and electromagnetic waves is impossible, when this medium shall have properties according to the principle of constant speed of light, that is, isotropy of speed of light in every system of reference.…
We consider transformations between uniformly accelerated systems, assuming that the Clock Hypothesis is false. We use the proper velocity-time description of events rather than the usual space-time description in order to obtain linear…
We study the process of compactification as a topology change. It is shown how the mediating spacetime topology, or cobordism, may be simplified through surgery. Within the causal Lorentzian approach to quantum gravity, it is shown that any…
We set up a covariant renormalisation group equation on a foliated spacetime which preserves background diffeomorphism symmetry. As a first application of the new formalism, we study the effect of quantum fluctuations in Lorentz symmetry…
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…
Radar-holonomic congruences of wordlines are proposed as a weaker substitute for the too restrictive class of Born-rigid motions. The definition is expressed as a set of differential equations. Integrability conditions and Cauchy data are…
The paper aims to introduce a new symmetry principle in the space-time geometry through the elimination of the classical idea of rest and by including a universal minimum limit of speed in the subatomic world. Such a limit, unattainable by…
In this letter we discuss the possibility of treating the spacetime by itself as a kind of deformable body for which we can define an fundamental lattice, just like atoms in crystal lattices. We show three signs pointing in that direction.…