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6.7. Anisotropic Fireballs

It is unlikely that a realistic fireball will be spherically symmetric. In fact strong deviation from spherical symmetry are expected in the most promising neutron star merger model, in which the radiation is expected to emerge through funnels along the rotation axis. The initial motion of the fireball might be fairly complex but once gamma >> 1 the motion of each fluid element decouples from the motion of its neighbors with angular distance larger than gamma-1. This motion can be described by the same asymptotic solution, as if it is a part of a spherical shell. We define the angular range over which different quantities vary as theta. Additionally now the motion is not radially outwards and ur neq u. We define the spread angle phi as ur ident u cosphi. The spherical fireball equations hold locally if:

Equation 28 (28)