EVOLUTION OF A HYPERSPATIAL TUBE DUE TO THE CASIMIR EFFECT

We study the time evolution of a hyperspatial tube (a cylinder if immersed in five dimensions). The time evolution is given by the Einstein equations. We assume that the only contributions to the energy-momentum tensor comes from the vacuum fluctuations (the zero-point energy). The time evolution for this space-time model is then determined from the Einstein equation. As it turns out, the tube is extremely unstable; it explodes or it implodes, at least in one direction. At later times, however, most hyperspatial tubes change from growing exponentially to power law growth. © 1995 The American Physical Society.