Figure 12: Proposal of [80] for the phase curves of thermal equilibrium phases in .
The solid lines and figures have significant arguments in their favor, while the dashed lines and figures
might not exist and admit conceivable, but more complicated, alternatives. Some features have been
drawn arbitrarily; at any given bifurcation, and in any dimension, smooth connections are possible
instead of swallowtails with cusps; also, the bifurcation into two black-Saturn phases may happen
before, after, or right at the merger with the pinched black hole. Mergers to di-rings or multiple-ring
configurations that extend to asymptotically large seem unlikely. If thermal equilibrium is not
imposed, the whole semi-infinite strip , is covered, and multiple
rings are possible.
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