Rotating black hole hair
  A Kerr black hole sporting cosmic string hair is studied in the context of
the abelian Higgs model vortex. It is shown that a such a system displays much
richer phenomenology than its static Schwarzschild or Reissner--Nordstrom
cousins, for example, the rotation generates a near horizon electric field. In
the case of an extremal rotating black hole, two phases of the Higgs hair are
possible: Large black holes exhibit standard hair, with the vortex piercing the
event horizon. Small black holes on the other hand, exhibit a flux-expelled
solution, with the gauge and scalar field remaining identically in their false
vacuum state on the event horizon. This solution however is extremely sensitive
to confirm numerically, and we conjecture that it is unstable due to a
supperradiant mechanism similar to the Kerr-adS instability. Finally, we
compute the gravitational back reaction of the vortex, which turns out to be
far more nuanced than a simple conical deficit. While the string produces a
conical effect, it is conical with respect to a local co-rotating frame, not
with respect to the static frame at infinity. As a consequence, we find that
the ergosphere is shifted, and geodesics around the black hole are perturbed.
