Photon regions and shadows of Kerr-Newman-NUT black holes with a cosmological constant

Abstract

We consider the Pleba\ifmmode \acute{n}\else \'{n}\fi{}ski class of electrovacuum solutions to the Einstein equations with a cosmological constant. These space-times, which are also known as the Kerr-Newman-NUT--(anti--)de Sitter space-times, are characterized by a mass $m$, a spin $a$, a parameter $\ensuremath{\beta}$ that comprises electric and magnetic charge, a NUT parameter $\ensuremath{\ell}$ and a cosmological constant $\mathrm{\ensuremath{\Lambda}}$. Based on a detailed discussion of the photon regions in these space-times (i.e., of the regions in which spherical lightlike geodesics exist), we derive an analytical formula for the shadow of a Kerr-Newman-NUT--(anti--)de Sitter black hole for an observer at given Boyer-Lindquist coordinates $({r}_{O},{\ensuremath{\vartheta}}_{O})$ in the domain of outer communication. We visualize the photon regions and the shadows for various values of the parameters.