Fast and accurate analytical formulas for light propagation in general static, spherically symmetric spacetimes

Abstract

In this article, we extend our previously presented analytical formulas [J. Claros and E. Gallo, [Phys. Rev. D 109, 124055 (2024)] ] for describing light rays passing near or emitted in the vicinity of compact objects to a broader class of spherically symmetric, static spacetimes, including the Johansen–Psaltis and Rezzolla-Zhidenko metric families. The generalized formulas retain the simplicity and accuracy of the original approach while allowing for more general deviations from Schwarzschild geometry. These expressions provide an approximate yet accurate mapping between emission points and the image plane of an asymptotic observer, enabling fast analytical computations of accretion disk images, polarization of the emitted radiation, luminosity curves associated with pulsars, and other related applications. As examples, we compute isoradial curves for several metric families and the Stokes parameters 𝑄 and 𝑈 for a hot spot orbiting near a black hole described by one of the studied metrics, presenting the corresponding polarization (𝑄⁢𝑈) curves.