There are many problems of black hole physics which require detailed knowledge of propagation of physical fields in the black hole geometry. In particular, they include:

● the radiation emitted by objects falling into a black hole,

● the gravitational radiation during a slightly non-spherical gravitational collapse,

● scattering and absorption of waves by a black hole,

● gravitational radiation from coalescing compact binary systems,

● analysis of stability of black hole solutions and

● quantum radiation of black holes.

For these and other relevant problems it is often sufficient to consider physical fields (including gravitational perturbations) in a linear approximation and to neglect their back reaction on the background black hole geometry.