  We propose and demonstrate a new and efficient approach to investigate black
hole dynamics in the limit of large number of dimensions $D$. The basic idea is
that an asymptotically flat black brane evolving under the Gregory-Laflamme
instability forms lumps that closely resemble a localized black hole. In this
manner, the large-$D$ effective equations for extended black branes can be used
to study localized black holes. We show that these equations have exact
solutions for black-hole-like lumps on the brane, which correctly capture the
main properties of Schwarzschild and Myers-Perry black holes at large $D$,
including their slow quasinormal modes and the ultraspinning instabilities
(axisymmetric or not) at large angular momenta. Furthermore, we obtain a novel
class of rotating `black bar' solutions, which are stationary when
$D\to\infty$, and are long-lived when $D$ is finite but large, since their
gravitational wave emission is strongly suppressed. The leading large $D$
approximation reproduces to per-cent level accuracy previous numerical
calculations of the bar-mode growth rate in $D=6,7$.
