Isaac Scientific Publishing
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
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
References
  • [1] Ying, L., Candes, E.J., "Fast Geodesics Computation with the Phase Flow Method," Jour. of Comp. Phys., 220, 1, pp 6-8 (2006).
  • [2] Vincent, F.H., Gourgoulhon, E. and Novak, J., "3+1 geodesic equation and images in numerical spacetimes," Class. Quantum Grav., 29, 245005, 1-17 (2012).
  • [3] Karas, V., Vokrouhlicky, D., Poinarev, A.G., "In the vicinity of a rotating black hole: a fast numerical code for computing observational effects," MNRAS, 259, 3, pp 569-575 (1992).
  • [4] Einstein, A., Relativity: The Special and General Theory, Methuen & Co. Ltd., London, UK (1916), trans. Lawson, R., Henry Holt & Co., NY (1920), p. 153.
  • [5] Ehlers, J. and Rindler, W., “Local and Global Light Bending in Einstein’s and other Gravitational Theories,” General Relativity and Gravitation, 29, 4 (1997).
  • [6] Einstein, A., "On the Influence of Gravitation on the Propagation of Light," Annalen der Physik, 35 (1911).
  • [7] Einstein, A., “The Foundation of the General Theory of Relativity,” Annalen der Physik, 49 (1916).
  • [8] Bodenner, J. and Will, C., “Deflection of light to second order: A tool for illustrating principles of general relativity,” Am. J. Phys., 71, 8 (2003).
  • [9] Taylor, J.H., Fowler, L.A. and McCulloch, P.M., “Measurements of general relativistic effects in the binary pulsar PSR1913+16,” Nature, 277, 8, pp. 437-440 (1979).
  • [10] Misner, C.W., Thorne, K.S. and Wheeler, J.A., Gravitation, W.H. Freeman & Co., San Francisco, p. 3 (1973).
  • [11] Kassner, K., "Classroom reconstruction of the Schwarzschild metric," Eur. J. Phys., 36, 6, pp. 31-50 (2015).
  • [12] Shapiro, I.I., Pettengill, G.H., Ash, M.E., Stone, M.L., Smith, W.B., Ingalls, R.P. and Brockelman, R.A., "Fourth Test of General Relativity: Preliminary Results," Phys. Rev. Lett., 20, 1265 (1968).
  • [13] Kopeikin, S.M. and Makarov, V.V., "Gravitational bending of light by planetary multipoles and its measurement with microarcsecond astronomical interferometers," Phys. Rev. D, 75, 6, p. 062002 (2007).
Copyright © 2017 Isaac Scientific Publishing Co. All rights reserved.