  We attempt to answer whether Birkhoff's theorem (BT) is valid in the
Einstein-Aether (EA) theory. The BT states that any spherically symmetric
solution of the vacuum field equations must be static, unique, and
asymptotically flat. For a general spherically symmetric metric with metric
functions $A(r,t)$ \& $B(r,t)$, and aether components $a(r,t)$ \& $b(r,t)$, we
prove the conditions for the staticity of spacetime using two different
methods. We point out that BT is valid in EA theory only for special values of
$c_1+c_3$, $c_1+c_4$, and $c_2$, where we can show that all these special cases
are asymptotically flat. In particular, when the aether has only a temporal
component, i.e., $b(r,t)=0$ and the $c_{14} \neq 0$ case gives us spherically
symmetric static black holes without horizons; that is, they have naked
singularities, at least for special values of $c_{14}$. Thus, the cosmic
censorship conjecture is violated for the case BT holds. However, when we have
an aether vector with temporal and radial components, we only prove that the
staticity and the flatness at infinity hold for a special metric and particular
combination of the aether parameters. For this case, there exist universal
horizons instead of naked singularities.
