The effect of spherical shells of matter on the Schwarzschild black hole

Based on previous work we show how to join two Schwarzschild solutions, possibly with different masses, along null cylinders each representing a spherical shell of infalling or outgoing massless matter. One of the Schwarzschild masses can be zero, i.e. one region can be flat. The above procedure can be repeated to produce space-times with a C ⁰ metric describing several different (possibly flat) Schwarzschild regions separated by shells of matter. An exhaustive treatment of the ways of combining four such regions is given; the extension to many regions is then straightforward. Cases of special interest are: (1) the scattering of two spherical gravitational “shock waves” at the horizon of a Schwarzschild black hole, and (2) a configuration involving only one external universe, which may be relevant to quantization problems in general relativity. In the latter example, only an infinitesimal amount of matter is sufficient to remove the “Wheeler wormhole” to another universe.