No static black hole hairs in gravitational theories of gravity with
  broken Lorentz invariance
  In this paper, we revisit the issue of static hairs of black holes in
gravitational theories with broken Lorentz invariance in the case that the
speed $c_{\phi}$ of the khronon field becomes infinitely large, $c_{\phi} =
\infty$, for which the sound horizon of the khronon field coincides with the
universal horizon, and the boundary conditions at the sound horizon reduce to
those given normally at the universal horizons. As a result, less boundary
conditions are present in this extreme case in comparison with the case
$c_{\phi} = $ finite. Then, it would be expected that static hairs might exist.
However, we show analytically that even in this case static hairs still cannot
exist, based on a decoupling limit analysis. We also consider the cases in
which $c_{\phi}$ is finite but with $c_{\phi} \gg 1$, and obtain the same
conclusion.
