  The time independent spherically symmetric solutions of General Relativity
(GR) coupled to a dynamical unit timelike vector are studied. We find there is
a three-parameter family of solutions with this symmetry. Imposing asymptotic
flatness restricts to two parameters, and requiring that the aether be aligned
with the timelike Killing field further restricts to one parameter, the total
mass. These "static aether" solutions are given analytically up to solution of
a transcendental equation. The positive mass solutions have spatial geometry
with a minimal area 2-sphere, inside of which the area diverges at a curvature
singularity occurring at an extremal Killing horizon that lies at a finite
affine parameter along a radial null geodesic. Regular perfect fluid star
solutions are shown to exist with static aether exteriors, and the range of
stability for constant density stars is identified.
