Gravitational Lensing by Charged Accelerating Black Holes

TL;DR

This paper explores how gravitational lensing can be used to detect electric charge in moving charged black holes described by the charged C-de Sitter metric, considering observational effects like lensing, travel time, and redshift.

Contribution

It introduces a method to observe electric charge in moving black holes through gravitational lensing using elliptic integrals and derived observables.

Findings

Electric charge affects gravitational lensing observables.

Derived lens equation, travel time, and redshift considering charge.

Discussed limitations in observing black hole charge.

Abstract

Current astrophysical observations show that on large scale the Universe is electrically neutral. However, locally this may be quite different. Black holes enveloped by a plasma in the presence of a strong magnetic field may have acquired a significant electric charge. We can also expect that some of these charged black holes are moving. Consequently to describe them we need spacetime metrics describing moving black holes. In general relativity such a solution is given by the charged C-de Sitter-metric. In this article we will assume that it can be used to describe moving charged black holes. We will investigate how to observe the electric charge using gravitational lensing. First we will use elliptic integrals and functions to solve the geodesic equations. Then we will derive lens equation, travel time and redshift. We will discuss the impact of the electric charge on these observables and potential limitations for its observation.