Matching Conditions and Gravitational Collapse in Two-Dimensional   Gravity
  The general theory of matching conditions is developed for gravitational theories in two spacetime dimensions. Models inspired from general relativity and from string theory are considered. These conditions are used to study collapsing dust solutions in spacetimes with non-zero cosmological constant, demonstrating how two-dimensional black holes can arise as the endpoint of such collapse processes. 
R.B. Mann and S.F. Ross