CLASSICAL SIGNATURE CHANGE IN THE BLACK-HOLE TOPOLOGY

Investigations of classical signature change have generally envisaged applications to cosmological models, usually a Friedmann-Lemaitre-Robe rtson-Walker mod el. The purpose has been to avoid the inevitable sing ularity of models with purely Lorentzian signature, replacing the neig hbourhood of the big bang with an initial, singularity free region of Euclidean signature, and a signature change. We here show that signatu re change can also avoid the singularity of gravitational collapse. We investigate the process of re-birth of Schwarzschild type black holes , modelling it as a double signature change, joining two universes of Lorentzian signature through a Euclidean region which provides a ''bou nce.'' We show that this process is viable both with and without matte r present, but realistic models - which have the signature change surf aces hidden inside the horizons - require nonzero density. In fact the most realistic models are those that start as a finite cloud of colla psing matter, surrounded by vacuum. We consider how geodesics may be m atched across a signature change surface, and conclude that the partic le ''masses'' must jump in value. This scenario may be relevant to Smo lin's recent proposal that a form of natural selection operates on the level of universes. which favours the type of universe we live in.