Approximating Light Rays in the Schwarzschild Field

Article

Approximating Light Rays in the Schwarzschild Field

Semerák, O.

ApJ 800(1), 77 (12 pp.) (2015)

Abstract

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.

Institute authors

Semerák, Oldřich

Supported by

GACR 14-10625S — General relativistic fields of compact astrophysical sources

BibTeX

@article{UTF564,
  author        = {Semerák, O.},
  title         = {{Approximating Light Rays in the Schwarzschild Field}},
  journal       = {ApJ},
  volume        = {800},
  number        = {1},
  pages         = {77 (12 pp.)},
  year          = {2015},
  month         = {2},
  doi           = {10.1088/0004-637X/800/1/77},
  url           = {https://iopscience.iop.org/article/10.1088/0004-637X/800/1/77},
}