Gauge theory at singularities

Abstract

Building on the author's previous results in singular semi-Riemannian geometry and singular general relativity, the behavior of gauge theory at singularities is analyzed. The usual formulations of the field equations at singularities are accompanied by infinities that block the evolution equations, mainly because the metric is singular, hence the usual differential operators, constructed from the metric, blow up. However, it is possible to give otherwise equivalent formulations of the Einstein, Maxwell, and Yang-Mills equations, which in addition admit solutions that can be extended beyond the singularities. The main purpose of this analysis is represented by applications to the black hole information loss paradox. An alternative approach can be made in terms of the Kaluza-Klein theory.