Odd-parity stability of black holes in Einstein-Aether gravity
  In Einstein-Aether theory, we study the stability of black holes against
odd-parity perturbations on a spherically symmetric and static background. For
odd-parity modes, there are two dynamical degrees of freedom arising from the
tensor gravitational sector and Aether vector field. We derive general
conditions under which neither ghosts nor Laplacian instabilities are present
for these dynamical fields. We apply these results to concrete black hole
solutions known in the literature and show that some of those solutions can be
excluded by the violation of stability conditions. The exact Schwarzschild
solution present for $c_{13} = c_{14} = 0$, where $c_i$'s are the four coupling
constants of the theory with $c_{ij}=c_i + c_j$, is prone to Laplacian
instabilities along the angular direction throughout the horizon exterior.
However, we find that the odd-parity instability of high radial and angular
momentum modes is absent for black hole solutions with $c_{13} = c_4 = 0$ and
$c_1 \geq 0$.
