The role of elliptic integrals in calculating the gravitational lensing of a charged Weyl black hole surrounded by plasma

TL;DR

This paper explores how elliptic integrals are crucial for calculating gravitational lensing effects caused by a charged Weyl black hole in a plasma medium, revealing complex dependencies on spacetime parameters.

Contribution

It demonstrates the application of elliptic integrals to model light deflection and black hole shadows in plasma environments around charged Weyl black holes, considering specific refractive index models.

Findings

Elliptic integrals effectively describe light deflection in plasma around black holes.

Different plasma models lead to varied dependencies of light behavior on spacetime parameters.

Photon sphere and black hole shadow characteristics are computed for specific refractive index cases.

Abstract

In this paper, we mainly aim at highlighting the importance of (hyper-)elliptic integrals in the study of gravitational effects caused by strongly gravitating systems. For this, we study the application of elliptic integrals in calculating the light deflection as it passes a plasmic medium, surrounding a charged Weyl black hole. To proceed with this, we consider two specific algebraic ansatzes for the plasmic refractive index, and we characterize the photon sphere for each of the cases. This will be used further to calculate the angular diameter of the corresponding black hole shadow. We show that the complexity of the refractive index expressions, can result in substantially different types of dependencies of the light behavior on the spacetime parameters.