Gravitational Lensing in the Charged NUT-de Sitter Spacetime

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.

v2: 41 pages and 16 figures; all figures in very high resolution; adapted to match publish version (except format and minor details); minor postprint changes to fix nonessential typos; part of this work is extended to massive particles in arXiv:2304.12563

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Cited by in corpus (5)

• Fermionic and Bosonic Greybody Factors as well as Quasinormal Modes for Charged Taub NUT Black Holes
• Gravitational Lensing of Massive Particles in the Charged NUT Spacetime
• Gravitational Lensing in the Kerr Spacetime: An Analytic Approach for Light and High-Frequency Gravitational Waves
• Accelerating electrically charged ModMax black hole solutions in $F(R)$ gravity
• The scalar angular Teukolsky equation and its solution for the Taub-NUT spacetime