Anomalous Fermion Production in Gravitational Collapse

TL;DR

This paper demonstrates the existence of a normalizable zero-energy fermion mode in a gravitational sphaleron background, linking topological transitions to fermion number anomalies during gravitational collapse.

Contribution

It reveals a novel fermion mode in Einstein-Yang-Mills backgrounds and connects topological vacuum transitions to fermion production in gravitational collapse.

Findings

Identification of a zero-energy fermion mode in the Einstein-Yang-Mills background.

Connection between sphaleron transitions and fermion number change.

Implication of fermion production during gravitational collapse.

Abstract

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