Figure 3: Phase space of (a) seven-dimensional, and (b) eight-dimensional MP rotating black holes
(in a representative quadrant ). The surfaces for extremal black holes are represented: black
holes exist in the region bounded by these surfaces. (a) : the hyperbolas at which the surface
intersects the planes (which are , i.e., and ) correspond
to naked singularities with zero area; otherwise, the extremal solutions are nonsingular. The three
prongs extend to infinity; these are the ultraspinning regimes in which one spin is much larger than
the other two. The prong along becomes asymptotically of the form , i.e.,
the same shape as the five-dimensional diagram in Figure 2(a). (b) : ultraspinning regimes
exist in which two spins are much larger than the third one. The sections at large constant
asymptotically approach the same shape as the six-dimensional phase space Figure 2(b).
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