Collapse of Kaluza-Klein bubbles

Kaluza-Klein theory admits ‘‘bubble’’ configurations, in which the circumference of the fifth dimension shrinks to zero on some compact surface. A three parameter family of such bubble initial data at a moment of time symmetry (some including a magnetic field) has been found by Brill and Horowitz, generalizing the (zero-energy) ‘‘Witten bubble’’ solution. Some of these data have negative total energy. We show here that all the negative energy bubble solutions start out expanding away from the moment of time symmetry, while the positive energy bubbles can start out either expanding or contracting. Thus it is unlikely that the negative energy bubbles would collapse and produce a naked singularity.