Related papers: Redshift and contact forms
We study the geometry of a weak Riemannian metric on the infinite dimensional manifold of compact spacelike Cauchy hypersurfaces in a globally hyperbolic spacetime. We show that the geodesic distance (i.e. the infimum of lengths of paths…
The relativity of cosmic time is developed within the framework of Cosmological Relativity in five dimensions of space, time and velocity. A general linearized metric element is defined to have the form $ds^2 = (1+\phi) c^2 dt^2 - dr^2 +…
Cosmic observations strongly support a time varying scenario for matter/space. On the other hand, so far, observations at solar system scale failed to identify any time variation on matter/space characteristics. To explain both results it…
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.…
Light rays received on earth from distant stars show redshift, being attributed conventionally to the well-known Doppler-effect of wave dynamics. The present study concludes that cosmic redshift rather is an effect of the quantum mechanical…
Gravitational redshift is discussed in the context of quantum photons propagating in curved spacetime. A brief introduction to modelling realistic photons is first presented and the effect of gravity on the spectrum computed for photons…
This paper gives a new proof that maximal, globally hyperbolic, flat spacetimes of dimension $n\geq 3$ with compact Cauchy hypersurfaces are globally foliated by Cauchy hypersurfaces of constant mean curvature, and that such spacetimes…
It is shown that for Robertson-Walker models with flat or closed space sections, all of the cosmological spectral shift can be attributed to the non-flat connection (and thus indirectly to space-time curvature). For Robertson-Walker models…
Fluid interfaces, such as soap films, liquid droplets or lipid membranes, are known to give rise to several special geometries, whose complexity and beauty continue to fascinate us, as observers of the natural world, and challenge us as…
The aim of this manuscript is to obtain rigidity and non-existence results for parabolic spacelike submanifolds with causal mean curvature vector field in orthogonally splitted spacetimes, and in particular, in globally hyperbolic…
In classes on cosmology, students are often told that photons stretch as space expands, but just how physical is this picture? Does space really expand? In this article, we explore the notion of the redshift of light with Einstein's general…
In the Minkowski space, we consider a compact, spacelike hypersurface with boundary, which can be written as a graph on a spacelike hyperplane. We prove that, if its $k$-th mean curvature is constant, and its boundary is on the hyperplane…
Extraordinary rays in a hyperbolic metamaterial behave as particle world lines in a three dimensional (2+1) Minkowski spacetime. We analyze electromagnetic field behavior at the boundaries of this effective spacetime depending on the…
We prove that any maximal globally hyperbolic spacetime locally modelled on the anti-de Sitter space of dimension 3, and admitting a closed Cauchy surface, admits a time function $\tau$, such that every fiber $\tau^{-1}(t)$ is a spacelike…
We have investigated the spatial distribution of quasars and its relationship with redshift by using the two-point correlation function, the variance of cell counts and the conditional density as a function of redshift. By comparing our…
Using a fully gauge-invariant approach, we compute for the first time in the literature relativistic effects on the redshift drift up to second order in cosmological perturbation theory. This is achieved by employing a set of light-cone…
In this article we explore the relationship between the systole and the diameter of closed hyperbolic orientable surfaces. We show that they satisfy a certain inequality, which can be used to deduce that their ratio has a (genus dependent)…
On the base of the hypothesis about a nature of the time as a dimension of alien Universe relation between alteration of time with coordinates $\frac{\partial t}{\partial x}$ and time {t} offered: $ \frac{\partial t} {\partial x} = H_{t} t$…
It is well known fact that gravitational field can alter the space-time structure and gravitational redshift is its one example. Electromagnetic field can also alter the space-time similar to gravitational field. So electromagnetic field…
Consider a symplectic surface in a three-dimensional contact manifold with boundary on Reeb orbits (periodic orbits of the Reeb vector field). We assume that the rotation numbers of the boundary Reeb orbits satisfy a certain inequality, and…