Gauge theory at singularities

TL;DR

This paper explores reformulations of gauge theories at singularities in spacetime, enabling solutions to extend beyond singularities, with implications for black hole information loss and alternative Kaluza-Klein approaches.

Contribution

It introduces equivalent formulations of Einstein, Maxwell, and Yang-Mills equations that remain well-defined at singularities, allowing for extended solutions beyond traditional limits.

Findings

Reformulated gauge equations avoid infinities at singularities

Solutions can be extended beyond singularities in these formulations

Potential applications to resolving black hole information paradox

Abstract

Building on 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 which 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 which can be extended beyond the singularities. The main purpose of this analysis are applications to the black hole information loss paradox. An alternative approach can be made in terms of the Kaluza-Klein theory.