Rings, ripples, and rotation: connecting black holes to black rings

A bstract Singly-spinning Myers-Perry black holes in d ≥ 6 spacetime dimensions are unstable for sufficiently large angular momentum. We numerically construct (in d = 6 and d = 7) two new stationary branches of lumpy (rippled) black hole solutions which bifurcate from the onset of this ultraspinning instability. We give evidence that one of these branches connects through a topology-changing merger to black ring solutions which we also construct numerically. The other branch approaches a solution with large curvature invariants. We are also able to compare the d = 7 ring solutions with results from finite-size corrections to the blackfold approach, finding excellent agreement.