The rich phenomenology of collective neutrino oscillations has been studied only in one-dimensional or spherically symmetric systems. Motivated by the nonspherical example of coalescing neutron stars, presumably the central engines of short gamma-ray bursts, we use the Liouville equation to formulate the problem for general source geometries. Assuming the neutrino ensemble displays self-maintained coherence, the problem once more becomes effectively one-dimensional along the streamlines of the overall neutrino flux. This approach for the first time provides a formal definition of the single-angle approximation frequently used for supernova neutrinos and allows for a natural generalization to nonspherical geometries. We study the explicit example of a disk-shaped source as a proxy for coalescing neutron stars.
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