Influence of Space-Time Curvature on the Light Propagation

Quantum Wave Mechanics, 2022

Light slows down in a medium due to photon’s EM field interaction with the EM energy density of the medium. Wavefront curvature is associated with light deflection and gravitational lensing. Curvature is induced by variation in the vacuum refractive index KPV locally altering the velocity of light resulting in wavefront retardation in regions of increased energy intensity. A general illustration of curved manifolds of a gravitational potential well and vacuum refractive index hill are depicted. In gravity-free region, Minkowski space is isomorphic to Euclidean tangent space. In a gravitational field, the energy density varies resulting in curved manifold parameter spaces while the tangent space of spacetime remains flat. Unlike embedding diagrams associated with illustration of spacetime curvature in GR, spacetime remains Euclidean while variables such as EM nodal distances and frequencies represented in tangent space exhibit dilation, contraction and curvature with an established physical causal means and demonstrable effect.

Physical Review D, 1999

The Frontiers Collection, 2009

It is shown that the complete description of the propagation of light in a gravitational field and in non-inertial reference frames in general requires an average coordinate and an average proper velocity of light. The need for an average coordinate velocity of light in non-inertial frames is demonstrated by considering the propagation of two vertical light rays in the Einstein elevator (in addition to the horizontal ray originally discussed by Einstein). As an average proper velocity of light is implicitly used in the Shapiro time delay (as shown in the Appendix) it is explicitly derived and it is shown that for a round trip of a light signal between two points in a gravitational field the Shapiro time delay not only depends on which point it is measured at, but in the case of a parallel gravitational field it is not always a delay effect. The propagation of light in rotating frames (the Sagnac effect) is also discussed and an expression for the coordinate velocity of light is derived. The use of this coordinate velocity naturally explains why an observer on a rotating disk finds that two light signals emitted from a point on the rim of the disk and propagating in opposite directions along the rim do not arrive simultaneously at the same point.

Physical Review D, 2012

We investigate the effects of light cone caustics on the propagation of linear scalar fields in generic four-dimensional spacetimes. In particular, we analyze the singular structure of relevant Green functions. As expected from general theorems, Green functions associated with wave equations are globally singular along a large class of null geodesics. Despite this, the "nature" of the singularity on a given geodesic does not necessarily remain fixed. It can change character on encountering caustics of the light cone. These changes are studied by first deriving global Green functions for scalar fields propagating on smooth plane wave spacetimes. We then use Penrose limits to argue that there is a sense in which the "leading order singular behavior" of a (typically unknown) Green function associated with a generic spacetime can always be understood using a (known) Green function associated with an appropriate plane wave spacetime. This correspondence is used to derive a simple rule describing how Green functions change their singular structure near some reference null geodesic. Such changes depend only on the multiplicities of the conjugate points encountered along the reference geodesic. Using σ(p, p ) to denote a suitable generalization of Synge's world function, conjugate points with multiplicity 1 convert Green function singularities involving δ(σ) into singularities involving ±1/πσ (and vice-versa). Conjugate points with multiplicity 2 may be viewed as having the effect of two successive passes through conjugate points with multiplicity 1. Separately, we provide an extensive review of plane wave geometry that may be of independent interest. Explicit forms for bitensors such as Synge's function, the van Vleck determinant, and the parallel and Jacobi propagators are derived almost everywhere for all non-singular four-dimensional plane waves. The asymptotic behaviors of various objects near caustics are also discussed.

Journal of Physics: Conference Series, 2010

The geometry of a light wavefront, evolving from a initial flat wavefront in the 3-space associated with a post-Newtonian relativistic spacetime, is studied numerically by means of the ray tracing method. For a discretization of the bidimensional light wavefront, a surface fitting technique is used to determine the curvature of this surface. The relationship between the intrinsic curvature of the wavefront and the change of the arrival time at different points on the Earth is also numerically discussed.

An Electromagnetic Wave Propagation Equation (EWPE) is proposed that is unconstrained by Einstein’s upper light speed limit. The hypothesis is that light and other electromagnetic waves are propagated in vacuum at a speed given by c2 = k/ɤ, where c = propagation speed of the electromagnetic wave, k is a constant and ɤ = the gravity field density, given by ɤ = M/r2, where M = the mass influencing the gravity and r = the distance from the center of the ‘M’ mass. This relationship, together with light path distortion due to gravitational rotation, is shown to explain the anomalies observed in the Pioneer 10/11 trajectories, the Explorer I, III and IV trajectory mismatch, as well as the orbital energy changes observed with near-earth flybys. This finding, if validated, will significantly impact the post-Einstein science framework and provides new perspectives for understanding the nature of the universe, including the particle/wave duality behavior of light and other electromagnetic phenomena.

Nuclear Physics B, 1998

We derive the wave equation obeyed by electromagnetic fields in curved space-time. We find that there are Riemann and Ricci curvature coupling terms to the photon polarisation which result in a polarisation-dependent deviation of the photon trajectories from null geodesics. Photons are found to have an effective mass in an external gravitational field and their velocity in an inertial frame

Progress In Electromagnetics Research M, 2016

An optical impedance-matched medium with a gradient refractive index can resemble a geometrical analogy with an arbitrary curved space-time. In this paper, we show that a non-impedancematched medium with a varying optical axis can also resemble the features of a space of non-trivial metric for the light. The medium with a varying optical axis is an engineered stratified slab of material, in which the orientation of the optical axis in each layer slightly differs from the other layers, while the magnitude of refractive index remains constant. Instead of the change in refractive index, the inhomogeneity of such a medium is induced by the local anisotropy. Therefore, the propagation of light depends on the local optical axis. We study the conditions that make the analogy between curved spacetime and a medium with a varying optical axis. Extension of the transformation optics to the media with optical axis profile might ease some fabrication difficulties of materials with gradient refractive index.

Physical Review D, 1997

We study the propagation of an electromagnetic field in a weak gravitational background generated by a rotating mass. The solution of the Maxwell equations beyond the geometrical optics shows, together with the well-known deflection and rotation of the polarization plane already present in the geometrical optics approximation, new classical dispersive effects. We analyze such effects at first order in the gravitational constant G. In the case of an incoming wave with linear polarization they consist in the development of a component of circular polarization, a breaking of the orthogonality of the electric and magnetic fields, and additional contributions to the deflection of the beam and the rotation of the polarization plane. ͓S0556-2821͑97͒06422-9͔

Astrophysical Journal, 1998

We describe a numerical algorithm that simulates the propagation of light in inhomogeneous universes. This algorithm computes the trajectories of light rays between the observer, located at redshift z = 0, and distant sources located at high redshift using the multiple lens plane method. The deformation and deflection of light beams as they interact with each lens plane are computed