Related papers: Affine sphere spacetimes which satisfy the relativ…
A new approach for arbitrary dimension to the Friedmann cosmological models is presented. Taking suitable changes of the parameters of the spacetime the harmonic motion equations appear, where the curvature determines the angular frequency.…
A general integral inequality is established for compact spacelike submanifolds of codimension two in the Lorentz-Minkowski spacetime under the assumption that the mean curvature vector field is parallel. This inequality is then used to…
We analyze strong gravitational lensing by a spherically symmetric mass distribution within the Einstein-Straus-de Sitter framework in a spatially open Universe with negative curvature ($k = -1$). Applying the theory to the lensed quasar…
The starting point of this work is the principle that all movement of particles and photons in the observable Universe must follow geodesics of a 4-dimensional space where time intervals are always a measure of geodesic arc lengths, i.e.…
We provide a classification of complete improper affine spheres with singularities (say \emph{improper affine fronts}) in unimodular affine three-space $\boldsymbol{R}^3$ whose total curvature is greater than or equal to $-6\pi$, and a…
A comprehensive analysis of general relativistic spacetimes which admit a shear-free, irrotational and geodesic timelike congruence is presented. The equations governing the models for a general energy-momentum tensor are written down.…
A notion of geometric symmetry is introduced that generalizes the classical concepts of Killing fields and other affine collineations. There is a sense in which flows under these new vector fields minimize deformations of the connection…
Can a simple microscopic model of space and time demonstrate Special Relativity as the macroscopic (aggregate) behavior of an ensemble ? The question will be investigated in three parts. First, it is shown that the Lorentz transformation…
We investigate the wave optics in spherically symmetric spacetimes: Schwarzschild black hole, spherical star with a perfect absorbing surface, and massless/massive Ellis wormholes. Assuming a point wave source, wave pattern and power…
In 1971 Feynman, Kislinger and Ravndal [1] proposed Lorentz-invariant differential equation capable to describe relativistic particle with mass and internal space-time structure. By making use of new variables that differentiate between…
We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…
In canonical gravity, the choice of a local time direction is not obviously compatible with local Lorentz invariance. One way to address this issue is to view gravity as a gauge theory on observer space, rather than spacetime. In a Lorentz…
The Finslerian post-Lorentzian kinematic transformations can explicitly be obtained under uni-directional breakdown of spatial isotropy, provided that the requirement that the relativistic unit hypersurface (indicatrix or mass shell) be a…
We show a closed Bach-flat Riemannian manifold with a fixed positive constant scalar curvature has to be locally spherical if its Weyl and traceless Ricci tensors are small in the sense of either $L^\infty$ or $L^{\frac{n}{2}}$-norm.…
Gravitational lensing by the light sphere of compact objects like black holes and wormholes will give us information on the compact objects. In this paper, we provide an improved strong deflection limit analysis in a general asymptotically…
Recent observations on the quasar absorption spectra supply evidence for the variation of the fine structure constant $\alpha$. In this paper, we propose another interpretation of the observational data on the quasar absorption spectra: a…
If the presence of a gravitational field breaks the Lorentz symmetry valid for special relativity, an "absolute motion" might be detectable. We summarize a scalar theory of gravity with a such "ether", which starts from a tentative…
Lensing in a spherically symmetric and static spacetime is considered, based on the lightlike geodesic equation without approximations. After fixing two radius values r_O and r_S, lensing for an observation event somewhere at r_O and static…
The GRAAL experiment could constrain the variations of the speed of light. The anisotropy of the speed of light may imply that the spacetime is anisotropic. Finsler geometry is a reasonable candidate to deal with the spacetime anisotropy.…
We present a framework for studying gravitational lensing in spherically symmetric spacetimes using 1+1+2 covariant methods. A general formula for the deflection angle is derived and we show how this can be used to recover the standard…