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Title: APPROXIMATING LIGHT RAYS IN THE SCHWARZSCHILD FIELD

A short formula is suggested that approximates photon trajectories in the Schwarzschild field better than other simple prescriptions from the literature. We compare it with various ''low-order competitors'', namely, with those following from exact formulas for small M, with one of the results based on pseudo-Newtonian potentials, with a suitably adjusted hyperbola, and with the effective and often employed approximation by Beloborodov. Our main concern is the shape of the photon trajectories at finite radii, yet asymptotic behavior is also discussed, important for lensing. An example is attached indicating that the newly suggested approximation is usable—and very accurate—for practically solving the ray-deflection exercise.
Authors:
 [1]
  1. Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague (Czech Republic)
Publication Date:
OSTI Identifier:
22364201
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 800; Journal Issue: 1; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; APPROXIMATIONS; ASYMPTOTIC SOLUTIONS; BLACK HOLES; COMPARATIVE EVALUATIONS; COSMIC PHOTONS; GRAVITATIONAL LENSES; POTENTIALS; RELATIVISTIC RANGE; SCHWARZSCHILD METRIC; VISIBLE RADIATION