Figure 6: Phase space of doubly-spinning black rings ( , ), restricted to the
representative region . The dashed line corresponds to extremal MP black
holes (see Figure 2(a)). The (upper) thin black curve corresponds to regular extremal black rings
with degenerate horizons at maximal spin , for given rotation . It ends on the
extremal MP curve at . The (lower) thick black curve corresponds to regular nonextremal
black rings with minimal spin along for given on . It ends on the extremal
MP curve at . Black rings exist in the gray-shaded parameter regions bounded by the
black curves, the segment of the extremal MP dashed line, and the axis with
. In the light-gray region there exist only thin black rings. In the dark-gray spandrel
between the dashed MP line, the thick black curve, and the axis , there exist thin
and fat black rings and MP black holes: there is discrete three-fold nonuniqueness.
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