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Advances in Astrophysics
AdAp > Volume 2, Number 1, August 2016

Numerical Geodesic Approximation for Theoretical and Experimental Light Bending Analysis

Download PDF  (469.9 KB)PP. 76-85,  Pub. Date:December 29, 2016

Robert L. Shuler
NASA Johnson Space Center, Houston, Texas, United States
This paper investigates a least-time (or fastest-path) two-point algorithm for numerically propagating a light ray in a gravitational field using anisotropic coordinate velocity and distantobserver coordinates. Rather than imaging or ray tracing, the objective is to support analysis of fundamentals and to be able to find null geodesics in arbitrary metrics. First we establish that results agree with geodesic paths in regard to bending angles to very high accuracy. Then we investigate the bending rate of two coordinate bending angles, wave and displacement, and find that wave angle illustrates well-known points about spatial and time components of light bending, while the displacement angle leads to simple analytic description of Einstein’s comment about the relation between these components, and a new figure showing the compatibility of light bending and equivalence. A second analysis compares light bending near a neutron star for Schwarzschild and one alternate metric to evaluate feasibility of future experiments. Two methods of extension to non-light speed objects are discussed.
gravity; light bending; space-time; curvature; equivalence; general relativity
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