Related papers: Redshift and contact forms
Vickers and Wilson (see Ref. 25) have shown global hyperbolicity of the conical spacetime in the sense of well-posedness of the initial value problem for the wave equation in generalized functions. We add the aspect of metric splitting and…
The classical phenomenon of the redshift of light in a static gravitational potential, usually called the gravitational redshift, is described in the literature essentially in two ways: on the one hand the phenomenon is explained through…
The Groups of causal and conformal automorphisms of globally hyperbolic spacetimes were studied. In two dimensions, we prove that all globally hyperbolic spacetimes that are directed and connected are causally isomorphic. We work out the…
The luminosity distance-redshift relation is one of the fundamental tools of modern cosmology. We compute the luminosity distance-redshift relation in a perturbed flat matter-dominated Universe, taking into account the presence of…
We observe that Khovanov homology detects causality in $(2+1)$-dimensional globally hyperbolic spacetimes whose Cauchy surface is homeomorphic to $\mathbb R^2$
To clarify some aspects of the application of Special Relativity, spacetime is sliced into null geodesic hypersurfaces as an alternative to the hypersurfaces of simultaneity normally adopted. Events at particle locations on the hypersurface…
An extension of the theory of General Relativity is proposed, based on pseudo-complex space-time coordinates. The new theory corresponds to the introduction of two, in general different, metrics which are connected through specific…
We investigate the effect of the redshift drift in strong gravitational lensing. The redshift drift produces a time variation of $i)$ the apparent position of a lensed source and $ii)$ the time delay among incoming signals from different…
We consider convex, spacelike hypersurfaces with boundaries on some hyperboloid (or lightcone) in the Minkowski space. If the hypersurface has constant higher order mean curvature, and the angle between the normal vectors of the…
There are now several analyses reporting quantized differences in the redshifts between pairs of galaxies. In the simplest cases, these differential redshifts are found to be harmonics of fundamental periods of approximately 72 km/s and…
Recent theoretical work determines the correct coupling constant of a scalar field to the Ricci curvature of spacetime in general relativity. The periodicity in the redshift distribution of galaxies observed by Broadhurst {\em et al.}, if…
No Hopf-Rinow Theorem is possible in Lorentzian Geometry. Nonetheless, we prove that a spacetime is globally hyperbolic if and only if it is metrically complete with respect to the null distance of a time function. Our approach is based on…
This paper presents alternative ideas on the physics of time that lead to a new interpretation of cosmological redshifts. These ideas are based on the close relationship between the speed of time and entropy processes in our universe. I…
We present a covariant approach to the problem of light beam propagation in a spacetime. We develop our considerations within the framework of classical geometric optics in general relativity. Using the concept of a screen surface…
The systolic ratio of a contact form on a closed three-manifold is the quotient of the square of the shortest period of closed Reeb orbits by the contact volume. We show that every co-orientable contact structure on any closed…
Hubble's correlation of red-shift with distance reveals that the universe is expanding, and that spacetime curvature has increased over time. And since time and space have equal status as dimensions, an object moving through time…
We investigate the distance-redshift relation in a realistic inhomogeneous universe where the mass distribution is described by the mass function of Sheth and Tormen. It is found that the derived distance deviates systematically from the…
Cosmological redshift z grows as the Universe expands and is conventionally viewed as a third form of redshift, beyond the more traditional Doppler and gravitational effects seen in other applications of general relativity. In this paper,…
Solutions of the Cauchy problem for the wave equation on a non-globally hyperbolic spacetime, which contains closed timelike curves (time machines) are considered. It is proved, that there exists a solution of the Cauchy problem, it is…
The phase shift due to the Sagnac Effect, for relativistic matter and electromagnetic beams, counter-propagating in a rotating interferometer, is deduced using two different approaches. From one hand, we show that the relativistic law of…