Geometry of null-like surfaces in general relativity and its application to dynamics of gravitating matter

Geometric tools describing the structure of a null-like surface S (wave front) are constructed. They are applied to the analysis of interaction between a light-like matter shell and the surrounding gravitational field. It is proved that the Einstein tensor Gab describing such a situation may be written in terms of external curvature of S. Conservation laws (Bianchi identities) for G are proved. Also geometry of isolated horizons (surfaces surrounding black holes) is analyzed in terms of the constructed tools. The possibility of application of these results to the problem of motion of isolated objects in general relativity is discussed.