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GR: Fachverband Gravitation und Relativitätstheorie

GR 1: Schwarze Löcher I

GR 1.8: Talk

Monday, February 25, 2013, 15:45–16:00, HS 6

Photon distribution near a static black hole — •Dennis Philipp¹ and Volker Perlick² — ¹Fachbereich Physik, Universität Bremen, 28359 Bremen — ²ZARM, Universität Bremen, 28359 Bremen

We consider the distribution of photons in die vicinity of a Schwarzschild black hole. As the initial condition, we assume that at each point of the sphere of radius r = R (for some large R) a monochromatic and isotropic flash of light is emitted at t=0. We use the concepts of kinetic theory, describing the photons in terms of a distribution function on 8-dimensional phase space P with coordinates (x^µ,p_µ). The resulting distribution function, which satisfies Liouville’s equation (the collisionless Boltzmann equation), is implicitly given by an equation that involves elliptic integrals. By integration over the momentum space we calculate the distribution function explicitly, in terms of elementary functions, in the limit t → ∞, and we show that it has a singularity at r=3m. We argue that every Schwarzschild black hole in Nature is surrounded by a sphere of very high photon density near r=3m which could be detrimental to the health of any observer that comes close to it.