Related papers: Parametrized post-post-Newtonian analytical soluti…
A fairly general expression for a light beam is found as a solution of the paraxial Helmholtz equation. It is achieved by exploiting appropriately chosen complex variables which entail the separability of the equation. Next, the expression…
In a recent investigation, the initial value problem of light propagation in the gravitational field of a body at rest with monopole and quadrupole structure has been determined in the second post-Newtonian (2PN) approximation. In reality,…
We propose new analytic formulae describing light bending in Schwarzschild metric. For emission radii above the photon orbit at 1.5 Schwarzschild radius, the formulae have an accuracy of better than 0.2% for the bending angle and 3% for the…
We extend a previous phenomenological analysis of photon lensing in an external gravitational background to the case of a massless neutrino, and propose a method to incorporate radiative effects in the classical lens equations of neutrinos…
In this investigation the light propagation in the gravitational field of one arbitrarily moving body with monopole structure is considered in the second post-Newtonian approximation. It is found that the light trajectory depends on the…
The present work describes some extensions of an approach, originally developed by V.V. Yatsyk and the author, for the theoretical and numerical analysis of scattering and radiation effects on infinite plates with cubically polarized…
A new formulation for light propagation in geometric optics by means of the Bi-local Geodesic Operators is considered. We develop the BiGONLight Mathematica package, uniquely designed to apply this framework to compute optical observables…
The first order post Newtonian scheme in multiple systems presented by Damour-Soffel-Xu is extended to the second order one for light propagation without changing the advantage of the scheme on the linear partial differential equations of…
This paper is the fourth in a series dedicated to the mathematically rigorous asymptotic analysis of gravitational radiation under astrophysically realistic setups. It provides an overview of the physical ideas involved in setting up the…
A new approach, which is based on the new canonical equations of Hamilton found by us recently, is presented to analytically obtain the approximate solution of the nonlocal nonlinear Schr\"{o}dinger equation (NNLSE). The approximate…
Using the matrix Riemann-Hilbert factorization approach for nonlinear evolution systems which take the form of Lax-pair isospectral deformations and whose corresponding Lax operators contain both discrete and continuous spectra, the…
Todays astrometry has reached the micro-arcsecond level in angular measurements of celestial objects. The next generations of astrometric facilities are aiming at the sub-micro-arcsecond scale. Sub-micro-arcsecond astrometry requires a…
In this paper, we extend the first-order post-Newtonian scheme in multiple systems presented by Damour-Soffel-Xu to the second-order contribution to light propagation without changing the virtueof the scheme on the linear partial…
We come back to the Cauchy integral equations occurring in radiative transfer problems posed in finite, plane-parallel media with light scattering taken as monochromatic and isotropic. Their solution is calculated following the classical…
Usual Gaussian beams are particular scalar solutions to the paraxial Helmholtz equation, which neglect the vector nature of light. In order to overcome this inconvenience, Simon et al. (J. Opt. Soc. Am. A 1986, 3, 536-540) found a paraxial…
Two long-standing problems with the post-Newtonian approximation for isolated slowly-moving systems in general relativity are: (i) the appearance at high post-Newtonian orders of divergent Poisson integrals, casting a doubt on the soundness…
We study the general relativistic non-linear dynamics of self-gravitating irrotational dust in a cosmological setting, adopting the comoving and synchronous gauge, where all the equations can be written in terms of the metric tensor of…
We study the Schr\"odinger equation which comes from the paraxial approximation of the Helmholtz equation in the case where the direction of propagation is tilted with respect to the boundary of the domain. In a first part, a mathematical…
A scalar, preferred-frame theory of gravitation is summarized. Space-time is endowed with both a flat metric and a curved, "physical" metric. Motion is governed by a natural extension of Newton's second law, which implies geodesic motion…
Using the matrix Riemann-Hilbert factorisation approach for non-linear evolution systems which take the form of Lax-pair isospectral deformations, the higher order asymptotics as $t \to \pm \infty$ $(x/t \sim {\cal O}(1))$ of the solution…