Advances in Astrophysics

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Volume 2, Number 1, August 2016

Numerical Geodesic Approximation for Theoretical and Experimental Light Bending Analysis
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76-85, Pub. Date:December 29, 2016

DOI:10.22606/adap.2016.12002

**Author(s)**
Robert L. Shuler

**Affiliation(s)**
NASA Johnson Space Center, Houston, Texas, United States

**Abstract**
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.

**Keywords**
gravity; light bending; space-time; curvature; equivalence; general relativity

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