Abstract
We discuss the construction ofperfect fluid stellar objects having optical geometries withmultiple necks corresponding to spatially closed unstablelightlike geodesics. We prove that physically reasonableequations of state can give rise to stellar equilibria witharbitrarily many necks. We also show how a first-order phasetransition can give rise to quite pronounced secondary necks.The analysis is carried out using a modification of a recentdynamical systems formulation of the TOV equations due toNilsson and Uggla. Our reformulation allows for a very generalfamily of equations of state including, for example, phasetransitions.
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