Figure 12

Figure 12: Proposal of [80] for the phase curves aH(j) of thermal equilibrium phases in d ≥ 6. 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 j seem unlikely. If thermal equilibrium is not imposed, the whole semi-infinite strip 0 < aH < aH(j = 0), 0 ≤ j < ∞ is covered, and multiple rings are possible.