GRAVITATIONAL TUNNELLING OF RELATIVISTIC SHELLS

Abstract

Thin shells in general relativity have been used in the past as keystones to obtain realistic models of cosmological and astrophysical situations. A crucial role for these developments was played by the compact description of their dynamics in terms of Israel’s junction conditions. Starting from this geometrical formulation we present a problem related to the WKB regime of shell dynamics and suggest a possible solution. General relativistic shells are an interesting system in general relativity and because of the simple geometrical description of their dynamics provided by Israel’s junction conditions [1] they became preferred models for many crucial aspects of astrophysical and cosmological situations (see [2] for a more complete bibliography on the subject). Many of these models have been developed under the assumption of spherical symmetry, but (as it happens for instance in the case of gravitational collapse [3]) this does not seem a severe restriction and it is likely that the obtained results can be extended to more general situations. On the other hand, the reduction in the number of degrees of freedom that it is possible to obtain in the spherically symmetric case makes simpler the development of effective models and more transparent the discussion of the interesting subtleties � To appear in the Proceedings of the 6th International Symposium on Frontiers in Funda