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Full-Text Articles in Physical Sciences and Mathematics
Deriving The Dyer-Roeder Equation From The Geodesic Deviation Equation Via The Newman-Penrose Null Tetrad, Aly Aly
Undergraduate Review
In this paper we examine the geodesic deviation equation using the Newman-Penrose (N-P) formalism for a flat Friedmann-Lemaitre-Robertson-Walker(FLRW) metric [Carroll,S. (2004), Ryden, B. (2003), Newman Penrose(1962)]. We solved the geodesic deviation equation for angular diameter distance, using the relevant N-P components, and the resulting expression was the Dyer-Roeder equation of cosmology [Ryden, B. (2003)] [Schneider et al.(1992)]. This leads us to believe that we can apply the N-P formalism to a perturbed FLRW metric and find a solvable equation for angular diameter distance [Kling Campbell(2008)]. The perturbed FLRW metric incorporates clumps of matter into a metric that is on average …
An Optical Scalar Approach To Weak Gravitation Lensing, Louis Bianchini
An Optical Scalar Approach To Weak Gravitation Lensing, Louis Bianchini
Undergraduate Review
We assume a thick gravitational lens governed by a Baltz n=1 matter density model. From the gravitational potential we then derive expressions for a Weyl tensor component and Ricci tensor component. A perturbative approach is taken to solve for the convergence and shear as given by Sach’s equation. By applying the geodesic deviation equation to a bundle of light rays with our expressions for the optical scalars we are able to derive expressions for the image shape and size at any point along the path from source to observer, in the case of an axially symmetric lens and source.
Modeling Weak Gravitational Lensing Through C++, Christopher Cepero
Modeling Weak Gravitational Lensing Through C++, Christopher Cepero
Undergraduate Review
Gravitational Lensing has become an integral part of astrophysics and the study of matter in the universe. In weak gravitational lensing, an object appears distorted when viewed from the observer’s perspective. This is caused by the bundle of light being distorted by an object of considerable mass. Because the distance to each part of this bundle is not the same, the rays of light are affected differently causing a shearing and magnification of the image. This alteration in the image we see can be modeled using the thin lens approximation. By integrating the equations for light travel based on general …