Contributed Talk - Splinter Compact

Thursday, 14 September 2023, 17:10   (H 2036)

Wave optical image formation of exact scalar wave scattering in Kerr-de Sitter spacetime

Felix Willenborg, Dennis Philipp, Claus Lämmerzahl
Zentrum für angewandte Raumfahrt und Mikrogravitation (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.