# SMuK 2023 – wissenschaftliches Programm

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# GR: Fachverband Gravitation und Relativitätstheorie

## GR 1: Black Holes

### GR 1.4: Vortrag

### Montag, 20. März 2023, 17:30–17:50, ZEU/0260

**Wave optical image formation of exact scalar wave scattering in Kerr-de Sitter spacetime** — •Felix Willenborg^{1}, Dennis Phillip^{1,2}, and Claus Lämmerzahl^{1,2} — ^{1}Zentrum für angewandte Raumfahrt und Mikrogravitation (ZARM), University of Bremen, 28359 Bremen, Germany — ^{2}Gauss-Olbers Center, c/o ZARM, University of Bremen, 28359 Bremen, Germany

Linear perturbations of black holes have been discussed widely in many contexts. Of interest are properties such as differential cross-sections, quasi-normal modes, scattering or the intereference. A useful tool in this respect is the Newman-Penrose formalism and the resulting Teukolsky equations, giving seperated angular and radial differential equations. These were mostly evaluated by numerical means. However, the introduction of a cosmological constant allows the problem to be solved in an exact analytical manner by transforming the differential equations into the Heun differential equation, the most general second-order differential equation with four regular singularities.

We show for the Kerr-de Sitter spacetime that scattering of waves from a point source needs an additational discussion around the so-called Heuns function, which enables a then possible normalization of the angular solution, similarly to the case of spherical harmonics. We assume in the discussion and analysis a scalar source star of fixed frequency and solve the scattering problem by a partial wave sum. The observed wave optical image formation by means of Kirchhoff-Fresnel diffraction and the resulting shadow will be compared to the geodesic black hole shadow.