Blue-Sheet Instability of Schwarzschild Wormholes

The Schwarzschild wormhole geometry is found to be unstable against the gravitational effects of accumulated, blue-shifted matter and radiation, or “blue sheets”, accreting along the past horizons. This is shown by constructing a simple model of a wormhole geometry featuring such blue sheets and manifesting their effects. In this model the blue sheets are treated as null delta-function surface layers, and we derive here general conditions for matching spacetime geometries across such null hypersurfaces of discontinuity. These junction conditions are then applied to the construction of the wormhole model. The wormhole evolution depicted in this model shows that the gravitational focussing produced by the blue-sheet mass-energy eventually encloses the blue sheets and past horizons within future horizons, leaving a black-hole geometry. These effects limit emission processes from the region of a wormhole’s past singularity into the external universe, and severely restrict the possible role of wormholes in cosmological contexts.