  We consider the evolution of a cosmic string loop that is captured by a much
more massive and compact black hole. We show that after several reconnections
that produce ejections of smaller loops, the loop that remains bound to the
black hole moves on a nearly-periodic non-self-intersecting trajectory, "the
orbit". The orbit evolves due to an energy and angular momentum exchange
between the loop and the spinning black hole. We show that such evolution is
mathematically equivalent to a certain continuous deformation of an auxiliary
closed curve in a 3-dimensional space; for zero black-hole spin this
deformation is curve-shortening that has been extensively studied by
mathematicians. The evolution features competing effects of loop growth by the
superradiant extraction of the black-hole spin energy, and loop decay by the
friction of the moving string against the horizon. A self-intersection of an
auxiliary curve corresponds to a capture by the black hole of a new string
segment and thus an addition of a new captured loop. Possible asymptotic states
of such evolution are shown to be strong emitters of gravitational waves.
Whether reconnections prevent reaching the asymptotic states remains to be
explored. Additionally, the orbit's shape also evolves due to an emission of
gravitational waves, and a recoil of the black hole that changes the orbit and
likely leads to self-intersections.
  We argue that for a significant range of the dimensionless tension $\mu$,
string loops are captured by supermassive black holes at the centers of
galaxies. This strongly motivates further study of interaction between string
loops and black holes, especially the influence of this process on the black
hole spindown and on the production of gravitational waves by strings created
in galactic nuclei. We also discuss potential loop captures by primordial black
holes.
