Gravitational collapse of a cylindrical null shell in vacuum

Barrabes -israel null shell formalism is used to study the gravitational collapse of a thin cylindrical null shell in vacuum. in generalthe lightlike matter shell whose history coincides with a null hypersurface is characterized by a surface energy density. in addition, agravitational impulsive wave is present on this null hypersurface whose generators admit both the shear and expansion. in the case ofimposing the cylindrical flatness the surface energy-momentum tensor of the matter shell on the null hypersurface vanishes and thenull hyper- surface is just the history of the gravitational wave.