Solitons and black holes in non-Abelian Einstein-Born-Infeld theory

TL;DR

This paper explores how Born-Infeld modifications to Einstein-Yang-Mills theory produce new soliton and black hole solutions, revealing a smooth interior structure that differs from traditional violent singularities, possibly due to quantum effects.

Contribution

It demonstrates a continuous connection between flat space solitons and black holes in Einstein-Born-Infeld theory and shows how non-linearity smooths black hole interiors.

Findings

Born-Infeld solutions relate to flat space solitons and black holes.

Black hole interiors are smooth with standard singularities.

No internal horizons observed in Born-Infeld black holes.

Abstract

Recently it was shown that the Born-Infeld-type modification of the quadratic Yang-Mills action gives rise to classical particle-like solutions in the flat space which have a striking similarity with the Bartnik-McKinnon solutions known in the gravity coupled Yang-Mills theory. We show that both families are continuously related within the framework of the Einstein-Born-Infeld theory through interpolating sequences of parameters. We also investigate an internal structure of the associated black holes. It is found that the Born-Infeld non-linearity leads to a drastic modification of the black hole interior typical for the usual Yang-Mills theory. In the latter case a generic solution exhibits violent metric oscillations near the singularity. In the Born-Infeld case a generic interior solution is smooth, the metric has the standard Schwarzschild type singularity, and we did not observe internal horizons. Such smoothing of the 'violent' EYM singularity may be interpreted as a result of quantum effects.