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Motions with respect to one inertial (or ``map'') frame are often described in terms of the coordinate time/velocity pair (or ``kinematic'') of the map frame itself. Since not all observers experience time in the same way, other…
We propose here that certain observational features of granular matter in the infrared limit, exhibiting the phenomenon of {\it jamming}, arise from an underlying effective general relativistic description. The proposal stems from the…
The images of many distant galaxies are displaced, distorted and often multiplied by the presence of foreground massive galaxies near the line of sight; the foreground galaxies act as gravitational lenses. Commonly, the lens equation, which…
A geometric theory for spacetimes whose world lines associated with physical particles have an upper bound for the proper acceleration is developed. After some fundamental remarks on the requirements that the classical dynamics for point…
We state a condition for an observer to be comoving with another observer in general relativity, based on the concept of lightlike simultaneity. Taking into account this condition, we study relative velocities, Doppler effect and light…
A model of relativistic extended particle is considered with the help of generalization of space-time inter-val. Ten additional dimensions are connected with six rotational and four deformational degrees of freedom. An obtained…
The equations of General Relativity are recast in the form of a wave equation for the Weyl tensor. This allows to reformulate gravitational wave theory in terms of curvature waves, rather than metric waves. The existence of two transverse…
We present a unified derivation of covariant time derivatives, which transform as tensors under a time-dependent coordinate change. Such derivatives are essential for formulating physical laws in a frame-independent manner. Three specific…
The problem of quantization of general relativity is considered in the framework of noncommutative differential geometry. Operator analogues for interval, scalar curvature, values of the Einstein tensor are proposed. Quantum measurements of…
General equations of the unified field theory, obtained using the curved and torsional space-time, are presented. They contain only independent geometrical parameters (metric and connections) of the metric-affine space, and describe the…
An analysis of composite inertial motion (relativistic sum) within the framework of special relativity leads to the conclusion that every translational motion must be the symmetrically composite relativistic sum of a finite number of quanta…
The present article deals with general mechanics in an unconventional manner. At first, Newtonian mechanics for a point particle has been described in vectorial picture, considering Cartesian, polar and tangent-normal formulations in a…
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
Non-perturbative studies of quantum gravity have recently suggested the possibility that the strength of gravitational interactions might slowly increase with distance. Here a set of generally covariant effective field equations are…
The relativistic acceleration of an electron in a uniform gravitational field is calculated numerically using the generalization of the Dirac equation to curved spacetime. Equivalent results are also obtained analytically using an iterative…
A four dimensional treatment of nonrelativistic space-time gives a natural frame to deal with objective time derivatives. In this framework some well known objective time derivatives of continuum mechanics appear as Lie-derivatives. Their…
Cosmography can be considered as a sort of a model-independent approach to tackle the dark energy/modified gravity problem. In this review, the success and the shortcomings of the $\Lambda$CDM model, based on General Relativity and standard…
We consider non-relativistic curved geometries and argue that the background structure should be generalized from that considered in previous works. In this approach the derivative operator is defined by a Galilean spin connection valued in…
General Relativity and its higher derivative extensions have symmetric teleparallel reformulations in terms of the non-metricity tensor within a torsion-free and flat geometry. These notes present a derivation of the exact propagator for…
Different (not only by sign) affine connections are introduced for contravariant and covariant tensor fields over a differentiable manifold by means of a non-canonical contraction operator, defining the notion dual bases and commuting with…