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The coupling between the electromagnetic and gravitational fields results in "faster than light" photons and invalids the Lorentz invariance and some laws of physics. A typical example is that the first and third laws of geometric optics…
In this paper shall we endeavour to substantiate that the evolution of the Riemann- Christoffel tensor or curvature tensor can be expressed entirely by an arbitrary timelike vector field and that the curvature tensor returns to its initial…
The problem of deforming geometries is particularly important in the context of constructing new exact solutions of Einstein's equation. This issue often appears when extensions of the general relativity are treated, for instance in brane…
Poincar\'e recurrence theorem implies the density of recurrent points for volume-preserving dynamical systems on compact domains. The density of closed orbits in the non-wandering set is one of the essential properties of Axiom A and chaos.…
Some foundational results on the geometry of Lorentz-Minkowski spaces and Finsler spacetimes are obtained. We prove that the local light cone structure of a reversible Finsler spacetime with more than two dimensions is topologically the…
The shortening of bodies in the direction of motion, Lorentz contraction, follows from the solution of Maxwell's equations. Moving light clocks will tick slower than those at rest because the speed of light does not depend on a source of…
One of the concepts of Relativity theory that challenges conventional intuition the most is time dilation and length contraction. Usual approaches for describing relativistic effects in quantum systems merely postulate the consequences of…
This article studies the N-vortex problem in the plane with positive vorticities. After an investigation of some properties for normalised relative equilibria of the system, we use symplectic capacity theory to show that, there exist…
As a sequel to (Berman, 2008a), we show that the rotation of the Universe can be dealt by generalised Gaussian metrics, defined in this paper. Robertson-Walker's metric has been employed with proper-time, in its standard applications; the…
This paper is a brief overview of a more extensive article recently published in Found. Phys. Lett. [2]. Apparent disagreement with experiment as well as internal inconsistencies found in the traditional analysis of relativistically…
We investigate the cosmological behavior in a universe governed by time asymmetric extensions of general relativity, which is a novel modified gravity based on the addition of new, time-asymmetric, terms on the Hamiltonian framework, in a…
In a recent paper, Mallett found a solution of the Einstein equations in which closed timelike curves (CTC's) are present in the empty space outside an infinitely long cylinder of light moving in circular paths around an axis. Here we show…
The issue of the "eternal return" is examined from the perspective of the topology of spacetime. Constraints on dynamical laws for the periodic evolution of a system or universe are highlighted. Using a Fourier series expansion, an infinite…
The theory of noncommutative geometry provides an interesting mathematical background for developing new physical models. In particular, it allows one to describe the classical Standard Model coupled to Euclidean gravity. However,…
The significance of past-pointing four-vectors and negative energies in general relativity is discussed. The sign of the energy is not absolute, but relative to the four-velocity of the observer, and every particle/observer always measures…
This paper completes and comments on some aspects of our previous publications. In ref [1], we have derived a set of space-time transformations referred to as the extended space-time transformations. These transformations, which assume the…
The missing of a Keplerian fall-off in the observed galaxy rotation curves represents classical evidence for the existence of dark matter on galactic scales. There has been some recent activity concerning the potential of modelling galactic…
The averaging problem in general relativity concerns the difficulty of defining meaningful averages of tensor quantities and we consider various aspects of the problem. We first address cosmological backreaction which arises because the…
A general theory of frames of reference proposed in a preceding publication is considered here in the framework of the post-Newtonian approximation, assuming that the frame of reference is centered on a time-like geodesic. The problem of…
In the Ashtekar and geometrodynamic formulations of vacuum general relativity, the Euclidean and Lorentzian sectors can be related by means of the generalized Wick transform discovered by Thiemann. For some vacuum gravitational systems in…