Scattering by a topological defect connecting two asymptotically Minkowski spacetimes

TL;DR

This paper investigates the stability and scattering of waves in a nontraversable wormhole spacetime connecting two Minkowski universes without exotic matter, revealing conditions for stability and resonance phenomena.

Contribution

It introduces a novel analysis of wave behavior on a topological defect connecting two flat spacetimes, emphasizing the role of boundary conditions in stability and scattering.

Findings

Identifies boundary conditions leading to stable scattering patterns.

Shows the spacetime can be stable without exotic matter.

Finds resonances at specific frequencies under certain boundary conditions.

Abstract

We study the stability and the scattering properties of a spacetime with a topological defect along a spherical bubble. This bubble connects two flat spacetimes which are asymptotically Minkowski, so that the resulting universe may be regarded as containing a wormhole. Its distinguished feature is the absence of exotic matter, i.e., its matter content respects all the energy conditions. Although this wormhole is nontraversable, waves and quantum particles can tunnel between both universes. Interestingly enough, the wave equation alone does not uniquely determine the evolution of scalar waves on this background, and the theory of self-adjoint extensions of symmetric operators is required to find the relevant boundary conditions in this context. Here we show that, for a particular boundary condition, this spacetime is stable and gives rise to a scattering pattern which is identical to the more usual thin-shell wormhole composed of exotic matter. Other boundary conditions of interest are also analyzed, including an unstable configuration with sharp resonances at well defined frequencies.