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Two interpretations of thin-shell instantons

For O(4)-symmetric instantons, there are two complementary interpretations for their analytic continuations. One is the nothing-to-something interpretation, where the initial and final hypersurfaces are disconnected by Euclidean manifolds. The other is the something-to-something interpretation, introduced by Brown and Weinberg, where the initial and final hypersurfaces are connected by the Euclidean manifold. These interpretations have their own pros and cons and hence they are complementary. In this paper, we consider analytic continuations of thin-shell instantons that have less symmetry, i.e., the spherical symmetry. When we consider the Farhi-Guth-Guven/Fischler-Morgan-Polchinski tunneling, the something-to-something interpretation has been used in the usual literature. On the other hand, we can apply the nothing-to-something interpretation with some limited conditions. We argue that for both interpretations, we can give the consistent decay rate. As we apply and interpret what follows the nothing-to-something interpretation, a stationary black hole can emit an expanding shell that results in a spacetime without a singularity or event horizon.