Collision of time-like shells in spherically symmetric spacetime

The spacetime representing a collision of two time-like shells is studied. This spacetime is constructed by 'cutting and pasting' four distinct Reissner-Nordstrom-de Sitter spacetimes. The junction condition is uniquely determined under the condition that the two colliding shells are transparent. In the limit of the collision of two neutral null shells, the junction condition reduces to the Dray-'t Hooft-Redmount (DTR) relation. The collision near the horizon is also investigated, and it is shown that phenomena like mass inflation do not occur unless one of the colliding shells is escaping from the horizon.