  We study spherical black-hole solutions in Einstein-aether theory, a
Lorentz-violating gravitational theory consisting of General Relativity with a
dynamical unit timelike vector (the "aether") that defines a preferred timelike
direction. These are also solutions to the infrared limit of Horava-Lifshitz
gravity. We explore parameter values of the two theories where all presently
known experimental constraints are satisfied, and find that spherical
black-hole solutions of the type expected to form by gravitational collapse
exist for all those parameters. Outside the metric horizon, the deviations away
from the Schwarzschild metric are typically no more than a few percent for most
of the explored parameter regions, which makes them difficult to observe with
electromagnetic probes, but in principle within reach of future
gravitational-wave detectors. Remarkably, we find that the solutions possess a
universal horizon, not far inside the metric horizon, that traps waves of any
speed relative to the aether. A notion of black hole thus persists in these
theories, even in the presence of arbitrarily high propagation speeds.
