Figure 3

Figure 3: Phase space of (a) seven-dimensional, and (b) eight-dimensional MP rotating black holes (in a representative quadrant ji ≥ 0). The surfaces for extremal black holes are represented: black holes exist in the region bounded by these surfaces. (a) d = 7: the hyperbolas at which the surface intersects the planes ji = 0 (which are √ -- jkjl = 1∕ 6, i.e., √ -- akal = μ and r0 = 0) 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 ji becomes asymptotically of the form |jk| + |jl| ≤ f(ji), i.e., the same shape as the five-dimensional diagram in Figure 2(a). (b) d = 8: ultraspinning regimes exist in which two spins are much larger than the third one. The sections at large constant ji asymptotically approach the same shape as the six-dimensional phase space Figure 2(b).