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Abstract
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.
Comments 27 pages, 6 figures; v2: minor editing, 1 new figure, references
added; v3: minor modification to abstract; v4: corrected overall sign in
twist formula and an error in equation for the aether stress tensor. Results
unchanged since correct form was used in calculations