  We study the well-posedness of the initial value (Cauchy) problem of vacuum
Einstein-aether theory. The latter is a Lorentz-violating gravitational theory
consisting of General Relativity with a dynamical timelike 'aether' vector
field, which selects a 'preferred time' direction at each spacetime event. The
Einstein-aether action is quadratic in the aether, and thus yields second order
field equations for the metric and the aether. However, the well-posedness of
the Cauchy problem is not easy to prove away from the simple case of
perturbations over flat space. This is particularly problematic because
well-posedness is a necessary requirement to ensure stability of numerical
evolutions of the initial value problem. Here, we employ a first-order
formulation of Einstein-aether theory in terms of projections on a tetrad
frame. We show that under suitable conditions on the coupling constants of the
theory, the resulting evolution equations can be cast into strongly or even
symmetric hyperbolic form, and therefore they define a well-posed Cauchy
problem.
