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

TL;DR

This paper develops generalized analytical formulas for light propagation in a wide class of static, spherically symmetric spacetimes, enabling fast and accurate modeling of astrophysical phenomena near compact objects.

Contribution

It extends previous formulas to include broader metric families, improving accuracy and applicability for simulating light behavior near various compact objects.

Findings

Derived formulas for multiple metric families including Johansen-Psaltis and Rezzolla-Zhidenko.

Validated the formulas by computing isoradial and polarization curves for different metrics.

Demonstrated the utility of formulas in modeling accretion disk images and polarization signals.

Abstract

In this article, we extend our previously presented analytical formulas (Phys.Rev.D 109 (2024) 12, 124055) 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 (QU) curves.