ANOMALOUS FERMION PRODUCTION IN GRAVITATIONAL COLLAPSE

The Dirac equation is solved in the Einstein-Yang-Mills background fou nd by Bartnik and McKinnon. We find a normalizable zero-energy fermion mode in the s-wave sector. As shown recently, their solution correspo nds to a gravitational sphaleron which mediates transitions between to pologically distinct vacua. Since the Bannik-McKinnon solution is unst able, it will either collapse to form a black hole or radiate away its energy. In either case, as the Chern-Simons number of the configurati on changes, there will be an accompanying anomalous change in fermion number.