  In Einstein-Aether gravity, we revisit the issue of linear stabilities of
black holes against odd-parity perturbations on a static and spherically
symmetric background. In this theory, superluminal propagation is allowed and
there is a preferred timelike direction along the unit Aether vector field. If
we choose the usual spherically symmetric background coordinates with respect
to the Killing time $t$ and the areal radius $r$, it may not be appropriate for
unambiguously determining the black hole stability because the constant $t$
hypersurfaces are not necessarily always spacelike. Unlike past related works
of black hole perturbations, we choose an Aether-orthogonal frame in which the
timelike Aether field is orthogonal to spacelike hypersurfaces over the whole
background spacetime. In the short wavelength limit, we show that no-ghost
conditions as well as radial and angular propagation speeds coincide with those
of vector and tensor perturbations on the Minkowski background. Thus, the
odd-parity linear stability of black holes for large radial and angular
momentum modes is solely determined by constant coefficients of the Aether
derivative couplings.
