Motivated by neutrino astronomy, we consider a plane wave of coupled and massive flavours, scattered by a static black hole, and describe analytically and numerically the corresponding oscillation probability in the surrounding space. Both the interpretation as particles travelling along geodesics and as scattered waves are studied, and consistently show a non-trivial and potentially long range interference pattern, in contrast to the spatially uniform transition probability in a flat

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... We introduce a numerical method for studying the oscillations around black holes, which accounts for the full curved geometry and flavour wave mixing. Whilst limited to the region immediately around the black hole, this numerical approach has the potential to be used in more general contexts, revealing the complex interference patterns which defy analytic methods.