Quantum Probe to the Higher Dimensional Yang-Mills Singularity

TL;DR

This paper examines the quantum nature of naked singularities in higher-dimensional Einstein-Yang-Mills theories, showing that higher curvature corrections can sometimes regularize these singularities.

Contribution

It demonstrates how Gauss-Bonnet corrections influence the quantum regularity of singularities in higher-dimensional EYM solutions, revealing dimension-dependent effects.

Findings

Gauss-Bonnet terms can render certain singularities quantum mechanically regular in 5D.

In dimensions ≥6, only secondary singularities may be healed, while central singularities remain quantum singular.

EYM and EMYM spacetimes are generally quantum mechanically singular without corrections.

Abstract

We investigate the quantum nature of naked curvature singularities in Einstein-Yang-Mills (EYM) theory using the Horowitz-Marolf (HM) criterion, which assesses quantum singularities via the evolution of quantum scalar fields. Focusing on timelike singularities in spacetime dimension $ D \geq 5 $, we analyze both pure Yang-Mills and Einstein-Maxwell-Yang-Mills (EMYM) solutions. We then incorporate higher curvature corrections through Gauss-Bonnet (GB) terms. From positivity requirement the expression under square root that arises in GB may create a secondary singularity that shall be scrutinized carefully. Our analysis reveals that while EYM and EMYM spacetimes remain quantum mechanically singular, the inclusion of GB corrections can, in general, render the singularity quantum mechanically regular for specific values of the mass parameter $m$, which is related to the YM charge $Q$ in $ D = 5 $ space-time dimensions. Contrary, for space-time dimension $D \geq 6$, although the outer (secondary) singularity may be healed quantum mechanically for certain values of the mass parameter $m$, the central singularity remains quantum mechanically singular.