# A new approximation of photon geodesics in Schwarzschild spacetime

## TL;DR

This paper presents a new approximation method for photon paths in Schwarzschild spacetime, accurately modeling highly bent trajectories near the black hole with less than 1% deviation from numerical solutions.

## Contribution

It introduces a novel approximation technique for photon geodesics that is especially accurate for trajectories behind the central mass, improving modeling near the ISCO.

## Key findings

- Deviation from numerical results below 1% up to ISCO
- Effective for highly bent photon trajectories
- Enhances computational efficiency in modeling photon paths

## 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 $6~GM/c^2$.