Orbits of light rays in scale-dependent gravity: Exact analytical solutions to the null geodesic equations

TL;DR

This paper derives exact analytical solutions for photon orbits in scale-dependent gravity, revealing how light trajectories and deflection angles depend on the running parameter, and compares these with other geometries.

Contribution

It provides the first explicit analytical solutions to null geodesics in scale-dependent gravity using Weierstra{} functions, enhancing understanding of light behavior in such spacetimes.

Findings

Exact solutions for null geodesics obtained in terms of Weierstra{} functions.

Light deflection angle depends on the scale-dependent parameter $\xi$.

An upper bound for the running parameter $\xi$ is established.

Abstract

We study photon orbits in the background of $(1+3)$-dimensional static, spherically symmetric geometries. In particular, we have obtained exact analytical solutions to the null geodesic equations for light rays in terms of the Weierstra{\ss} function for space-times arising in the context of scale-dependent gravity. The trajectories in the $(x-y)$ plane are shown graphically, and we make a comparison with similar geometries arising in different contexts. The light deflection angle is computed as a function of the running parameter $\xi$, and an upper bound for the latter is obtained.