Wave optical imaging by point-source scattering for a TNdS black hole

TL;DR

The paper develops a wave-optical imaging framework for Taub-NUT-de Sitter black holes by solving the Teukolsky master equation exactly. It separates the equation into angular and radial parts, converting them to (confluent) Heun equations and building a Green's function via a double-mode expansion with eigenvalue $\lambda_{nm}$. A Kirchhoff-Fresnel approach then yields observables on a plane, revealing constructive/destructive interference near semi-infinite singularities for single sources and potential elliptical wave-optical shadows for multi-source configurations, contrasting with ray-optical predictions. These results highlight richer wave-optical structure in nontrivial spacetimes and inform interpretations of black-hole shadows beyond ray optics.

Abstract

In our work, we present a calculation based on an exact, non-approximated wave equation, as described by the Teukolsky equation, for a Taub-NUT-de Sitter spacetime. We observe the scattering of a monochromatic point source by an observer located at a greater distance from the black hole, and examine the wave-optical images by a single source and by multiple sources.

Figures (2)

• Figure 1: a) Coordinate observer plane-point source alignment, b) Regularly distributed sources by Lebedev quadrature on an half sphere
• Figure 2: Variation of $N$ for fixed $M\omega = 8$, $C = 0$. a)-c): Single point-source, d)-f): multiple point-sources, see \ref{['TMESol:Scatter:Fig:Schemes:Mult']}. Orange-dashed lines are ray-optical shadow predictions by Ref. Grenzebach2016.