  Quasinormal modes in the high frequency (eikonal) regime can be obtained
analytically as the Mashhoon-Will-Schiutz WKB formula is exact in this case.
This regime is interesting because of the correspondence between eikonal
quasinormal modes and null geodesics, as well as due to existence of potential
eikonal instabilities in some theories of gravity. At the same time in a number
of studies devoted to quasinormal modes of spherically symmetric black holes
this opportunity was omitted. Here we find analytical quasinormal modes of
black holes in various alternative and extended theories of gravity in the form
of the Schwarzschld eikonal quasinormal modes and added corrections due to
deviations from Einstein theory. We also deduce a generic formula for
analytical calculations of the eikonal quasinormal modes for the class of
asymptotically flat metrics in terms of small deviations from the Schwarzschild
geometry.
