  In this paper, we investigate the asymptotic nature of the quasinormal modes
for "dirty" black holes -- generic static and spherically symmetric spacetimes
for which a central black hole is surrounded by arbitrary "matter" fields. We
demonstrate that, to the leading asymptotic order, the [imaginary] spacing
between modes is precisely equal to the surface gravity, independent of the
specifics of the black hole system.
  Our analytical method is based on locating the complex poles in the first
Born approximation for the scattering amplitude. We first verify that our
formalism agrees, asymptotically, with previous studies on the Schwarzschild
black hole. The analysis is then generalized to more exotic black hole
geometries. We also extend considerations to spacetimes with two horizons and
briefly discuss the degenerate-horizon scenario.
