Berlin 2015 – wissenschaftliches Programm

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GR: Fachverband Gravitation und Relativitätstheorie

GR 18: Black Holes

GR 18.1: Vortrag

Freitag, 20. März 2015, 11:10–11:30, H 2013

On wave propagation in Schwarzschild spacetime — •Dennis Philipp and Volker Perlick — ZARM, Universität Bremen, 28359 Bremen

The propagation of (massless) scalar, electromagnetic and gravitational waves on fixed Schwarzschild background spacetime is described by the general time-dependent Regge-Wheeler equation. We transform this wave equation to usual Schwarzschild, Eddington-Finkelstein and Painlevé-Gullstrand coordinates. After separating a harmonic time-dependence the resulting radial equations belong to the class of confluent Heun equations, i.e., we can identify two regular and one irregular singularities. Using the generalized Riemann-scheme we collect properties of all singular points and construct (local) solutions in terms of the standard confluent Heun function HeunC, Frobenius- and asymptotic Thomé series.

We study the Eddington-Finkelstein and Painlevé-Gullstrand cases in detail and obtain in each case a solution that is regular at the black hole horizon. This solution is connected to causal boundary conditions, i.e., purely ingoing radiation at r=2M. To construct solutions on the entire open interval r   ∈   ]0,∞[ we give an analytic continuation of local solutions around the horizon. Black hole scattering and quasi-normal modes are briefly considered as possible applications.