An order-disorder phase transition in black-hole star clusters
  The centers of most galaxies contain massive black holes surrounded by dense
star clusters. The structure of these clusters determines the rate and
properties of observable transient events, such as flares from tidally
disrupted stars and gravitational-wave signals from stars spiraling into the
black hole. Most estimates of these rates enforce spherical symmetry on the
cluster. Here we show that, in the course of generic evolutionary processes, a
star cluster surrounding a black hole can undergo a robust phase transition
from a spherical thermal equilibrium to a lopsided equilibrium, in which most
stars are on high-eccentricity orbits with aligned orientations. The rate of
transient events is expected to be much higher in the ordered phase. Better
models of cluster formation and evolution are needed to determine whether
clusters should be found in the ordered or disordered phase.
