Israel's Formalism: The Metric Junction Method

A question that often arises in gravitational theory is what happens to the geometry of spacewhen there is a jump discontinuity in the energy-momentum tensor along a surface. For example, what is the connection between the curvature properties for the interior Schwarzschild solution and the exterior Schwarzschild solution? Here, along the boundary of some surface, the energy density experiences a jump discontinuity. Another analogous scenario is for example a shock wave propagating outwards from an exploding star. In models of such shock waves the density can be infinite.