Geometry of null-like surfaces in General Relativity and its application to dynamics of

Geometric tools describing the structure of a null-like surface S (wave front) are constructed. They are applied to analysis of interaction between a light-like matter shell and the surrounding gravitational field. It is proved that the Einstein tensorGab 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 non-expanding horizons (surfaces surrounding black holes) is analyzed in terms of the constructed tools. Possibility of application of these results to the problem of motion of isolated objects in General Relativity is discussed. Key Words: general relativity, differential geometry, black holes Dedicated to Professor Roman S. Ingarden in honour of his 80-th birth-day