A new approximation of photon geodesics in Schwarzschild spacetime

Abstract

In this research note we introduce a new approximation of photon geodesics in Schwarzschild spacetime which is especially useful to describe highly bent trajectories, for which the angle between the initial emission position and the line of sight to the observer approaches $\pi$: this corresponds to the points behind the central mass of the Schwarzschild metric with respect to the observer. The approximation maintains very good accuracy overall, with deviations from the exact numerical results below $1\%$ up to the innermost stable circular orbit (ISCO) located at $6GM/c^2$.

arXiv comment3 pages, 1 figure, 3 subfigures

References in corpus (5)

• Gravitational Bending of Light Near Compact Objects
• Pulse profiles of millisecond pulsars and their Fourier amplitudes
• Rotational Broadening of Atomic Spectral Features from Neutron Stars
• Approximate analytical calculations of photon geodesics in the Schwarzschild metric
• Approximating light rays in the Schwarzschild field

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• Accurate analytical modeling of light rays in spherically symmetric spacetimes: Applications in the study of black hole accretion disks and polarimetry
• Neutron Star Radius-to-mass Ratio from Partial Accretion Disc Occultation as Measured through Fe K$\alpha$ Line Profiles
• Fast and accurate analytical formulas for light propagation in general static, spherically symmetric spacetimes