A note on the Penrose junction conditions

Impulsive pp-waves are commonly described either by a distributional spacet ime metric or, alternatively, by a continuous one. The transformation T rel ating these forms clearly has to be discontinuous, which causes two basic p roblems. First, it changes the manifold structure and second, the pullback of the distributional form of the metric under T is not well defined within classical distribution theory. Nevertheless, from a physical point of view both pictures are equivalent. In this work, after calculating T as well as the 'Rosen' form of the metric in the general case of a pp-wave with arbit rary wave profile we give a precise meaning to the term 'physically equival ent' by interpreting T as the distributional limit of a suitably regularize d sequence of diffeomorphisms. Moreover, it is shown that T provides an exa mple of a generalized coordinate transformation in the sense of Colombeau's generalized functions.