Orbits of light rays in (1+2)-dimensional Einstein-power-Maxwell gravity: Exact analytical solution to the null geodesic equations

TL;DR

This paper derives exact analytical solutions for photon orbits in a (1+2)-dimensional Einstein-power-Maxwell gravity setting, revealing how charge, energy, and initial conditions influence light trajectories.

Contribution

It provides the first exact analytical solutions to null geodesic equations in this specific non-linear electrodynamics context.

Findings

Photon orbits are expressed in terms of Weierstra{} functions.

Photon energy and black hole charge significantly affect orbit shapes.

Initial conditions alter the photon trajectory configurations.

Abstract

We study photon orbits within (1+2)-dimensional Einstein-power-Maxwell non-linear electrodynamics assuming a static and circularly symmetric background. An exact analytical solution to the null geodesic equations for light rays is obtained in terms of the Weierstra{\ss} function. We investigate in detail the impact of the photon energy, the electric charge of the black hole, and the integration constant (initial condition) on the shape of the orbits.