APPROXIMATING LIGHT RAYS IN THE SCHWARZSCHILD FIELD

Journal Article · Tue Feb 10 00:00:00 EST 2015 · Astrophysical Journal

DOI:https://doi.org/10.1088/0004-637X/800/1/77· OSTI ID:22364201

Semerák, O., E-mail: [e-mail] ^[1]

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1. Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague (Czech Republic)

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.

• OSTI ID: 22364201
• Journal Information: Astrophysical Journal, Vol. 800, Issue 1; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 0004-637X
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
APPROXIMATIONS
ASYMPTOTIC SOLUTIONS
BLACK HOLES
COMPARATIVE EVALUATIONS
COSMIC PHOTONS
GRAVITATIONAL LENSES
POTENTIALS
RELATIVISTIC RANGE
SCHWARZSCHILD METRIC
VISIBLE RADIATION