  We study black hole solutions in general relativity coupled to a unit
timelike vector field dubbed the "aether". To be causally isolated a black hole
interior must trap matter fields as well as all aether and metric modes. The
theory possesses spin-0, spin-1, and spin-2 modes whose speeds depend on four
coupling coefficients. We find that the full three-parameter family of local
spherically symmetric static solutions is always regular at a metric horizon,
but only a two-parameter subset is regular at a spin-0 horizon. Asymptotic
flatness imposes another condition, leaving a one-parameter family of regular
black holes. These solutions are compared to the Schwarzschild solution using
numerical integration for a special class of coupling coefficients. They are
very close to Schwarzschild outside the horizon for a wide range of couplings,
and have a spacelike singularity inside, but differ inside quantitatively. Some
quantities constructed from the metric and aether oscillate in the interior as
the singularity is approached. The aether is at rest at spatial infinity and
flows into the black hole, but differs significantly from the the 4-velocity of
freely-falling geodesics.
