Related papers: Analytical solution for light propagation in Schwa…
Numerical integration of the differential equations of light propagation in the Schwarzschild metric shows that in some situations relevant for practical observations the well-known post-Newtonian solution for light propagation has an error…
An analytical solution for light propagation in the post-post-Newtonian approximation is given for the Schwarzschild metric in harmonic gauge augmented by PPN and post-linear parameters $\beta$, $\gamma$ and $\epsilon$. The solutions of…
A rigorous analytical solution of light propagation in Schwarzschild metric in post-post Newtonian approximation has been presented in \cite{report1}. In \cite{report2} it has been asserted that the sum of all those terms which are of order…
In this investigation the boundary value problem of light propagation in the gravitational field of one arbitrarily moving body with monopole structure is considered in the second post-Newtonian approximation. The solution of the boundary…
We develop a method for deriving approximate analytical formulae to integrate photon geodesics in a Schwarzschild spacetime. Based on this, we derive the approximate equations for light bending and propagation delay that have been…
The paper deals with a special kind of problems that appear in solutions of Einstein's field equations for extended bodies: many structure-dependent terms appear in intermediate calculations that cancel exactly in virtue of the local…
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…
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 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. This model has been proposed in…
The relativistic theories of light propagation are generalized by introducing two new parameters $\varsigma$ and $\eta$ in the second post-Newtonian (2PN) order, in addition to the parameterized post-Newtonian parameters $\gamma$ and…
We present a method of post-Newtonian expansion to solve the homogeneous Regge-Wheeler equation which describes gravitational waves on the Schwarzschild spacetime. The advantage of our method is that it allows a systematic iterative…
One of the most subtle points in the modern relativistic models for microarcsecond astrometrical observations is the treatment of the influence of translational motion of gravitating bodies on the light propagation. This paper describes…
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,…
A generalized lens equation for weak gravitational fields in Schwarzschild metric and valid for finite distances of source and observer from the light deflecting body is suggested. The magnitude of neglected terms in the generalized lens…
The linear intensity profile of multiply scattered light in a slab geometry extrapolates to zero at a certain distance beyond the boundary. The diffusion equation with this "extrapolated boundary condition" has been used in the literature…
An analytical solution for the light trajectory in the near-zone of the gravitational field of one pointlike body in arbitrary slow-motion in the post-post-Newtonian approximation is presented in harmonic gauge. Expressions for total light…
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…
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…
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…
The post-Newtonian (PN) perturbative framework has been successful in understanding the slow-motion, weak field limit of Einstein's theory of gravity on solar system scales, and for isolated astrophysical systems. The parameterized…