  The local Lorentz violation (LV) in gravity sector should show itself in
derivation of the characteristic quasinormal modes (QNMs) of black hole mergers
from their general relativity case. In this paper, I study QNMs of the
gravitational field perturbations to Einstein-aether black holes and, at first
compare them to those in Schwarzschild black hole, and then some other known LV
gravity theories. By comparing to Schwarzschild black hole, the first kind
aether black holes have larger damping rate and the second ones have lower
damping rate. And they all have smaller real oscillation frequency of QNMs. By
comparing to some other LV theories, the QNMs of the first kind aether black
hole are similar to that of the QED-extension limit of standard model
extension, non-minimal coupling to Einstein's tensor and massive gravity
theories. While as to the second kind aether black hole, they are similar to
those of the noncommutative gravity theories and Einstein-Born-Infeld theories.
These similarities may imply that LV in gravity sector and LV in matter sector
have some intrinsic connections.
