Approximating light rays in the Schwarzschild field

Abstract

A short formula is suggested which 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 behaviour 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.

13 pages, 6 figures

References in corpus (5)

• Relativistic images of Schwarzschild black hole lensing
• Geodesic equation in Schwarzschild--(anti-)de Sitter space--times: Analytical solutions and applications
• Strong gravitational lensing from compact bodies: analytical results
• Particles under radiation thrust in Schwarzschild space-time from a flux perpendicular to the equatorial plane
• Ray-tracing in four and higher dimensional black holes: An analytical approximation

Cited by in corpus (4)

• Testing wormhole solutions in extended gravity through the Poynting-Robertson effect
• General relativistic Poynting-Robertson effect to diagnose wormholes existence: static and spherically symmetric case
• Particles under radiation thrust in Schwarzschild space-time from a flux perpendicular to the equatorial plane
• Position determination and strong field parallax effects for photon emitters in the Schwarzschild spacetime