We argue that the event horizon of a binary black hole merger, in the extreme-mass-ratio limit where one of the black holes is much smaller than the other, can be described in an exact analytic way. This is done by tracing in the Schwarzschild geometry a congruence of null geodesics that approaches a null plane at infinity. Its form can be given explicitly in terms of elliptic functions, and we use it to analyze and illustrate the time-evolution of the horizon along the merger. We identify features such as the line of caustics at which light rays enter the horizon, and the critical point at which the horizons touch. We also compute several quantities that characterize these aspects of the merger.

We study six-dimensional rotating black holes with bumpy horizons: these are topologically spherical, but the sizes of symmetric cycles on the horizon vary non-monotonically with the polar angle. We construct them numerically for the first three bumpy families, and follow them in solution space until they approach critical solutions with localized singularities on the horizon. We find strong evidence of the conical structures that have been conjectured to mediate the transitions to black rings, to black Saturns, and to a novel class of bumpy black rings. For a different, recently identified class of bumpy black holes, we find evidence that this family ends in solutions with a localized singularity that exhibits apparently universal properties, and which does not seem to allow for transitions to any known class of black holes.Comment: 24 pages, 33 figures. v2: published versio

We construct solutions of non-uniform black strings in dimensions from D ≈ 9 all the way up to D = ∞, and investigate their thermodynamics and dynamical stability. Our approach employs the large-D perturbative expansion beyond the leading order, including corrections up to 1/D 4 . Combining both analytical techniques and relatively simple numerical solution of ODEs, we map out the ranges of parameters in which non-uniform black strings exist in each dimension and compute their thermodynamics and quasinormal modes with accuracy. We establish with very good precision the existence of Sorkin's critical dimension and we prove that not only the thermodynamic stability, but also the dynamic stability of the solutions changes at it.

We present a simple, general, and accurate construction of the event horizons for the fusion of two neutral, rotating black holes with arbitrary orientation and values of their spins, in the extreme mass ratio limit where one black hole is much larger than the other. We compute several parameters that characterize the fusion and investigate their dependence on the black hole spin and orientation axis. We also exhibit and study the appearance of transient toroidal topology of the horizon. An earlier conjecture about universal critical exponents before and after an axisymmetric pinch is proven.