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GR: Fachverband Gravitation und Relativitätstheorie
GR 1: Black Holes
GR 1.4: Talk
Monday, March 20, 2023, 17:30–17:50, ZEU/0260
Wave optical image formation of exact scalar wave scattering in Kerr-de Sitter spacetime — •Felix Willenborg1, Dennis Phillip1,2, and Claus Lämmerzahl1,2 — 1Zentrum für angewandte Raumfahrt und Mikrogravitation (ZARM), University of Bremen, 28359 Bremen, Germany — 2Gauss-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.