Gravitational Lensing in the Charged NUT-de Sitter Spacetime

TL;DR

This paper investigates how gravitational lensing can be used to detect gravitomagnetic charges in black holes described by the charged NUT-de Sitter spacetime, providing new methods to observe such exotic features.

Contribution

It derives the equations for lightlike geodesics in charged NUT-de Sitter spacetime and explores observational signatures of gravitomagnetic charges through lensing effects.

Findings

Derived the equations of motion for light in this spacetime.

Analyzed the black hole shadow and lens map in the presence of gravitomagnetic charge.

Discussed observational differences from spherically symmetric black holes.

Abstract

It is a long-standing open question if a gravitomagnetic charge, the gravitational analogon to a hypothetical magnetic charge in electrodynamics, exists in nature. It naturally occurs in certain exact solutions to Einstein's electrovacuum-field equations with cosmological constant. The charged NUT-de Sitter metric is such a solution. It describes a black hole with electric and gravitomagnetic charges and a cosmological constant. In this paper we will address the question how we can observe the gravitomagnetic charge using gravitational lensing. For this purpose we first solve the equations of motion for lightlike geodesics using Legendre's canonical forms of the elliptic integrals and Jacobi's elliptic functions. We fix a stationary observer in the domain of outer communication and introduce an orthonormal tetrad. The orthonormal tetrad relates the direction under which the observer detects a light ray to its latitude-longitude coordinates on the observer's celestial sphere. In this parametrization we rederive the angular radius of the shadow, formulate a lens map, discuss the redshift, and the travel time. We also discuss relevant differences with respect to spherically symmetric and static spacetimes and how we can use them to determine if an astrophysical black hole has a gravitomagnetic charge.