Smooth metrics for snapping strings

TL;DR

This paper develops smooth metrics for abelian Higgs vortices ending on black holes, showing how vortex field details smooth out singularities and exploring implications for string stability and black hole pair production.

Contribution

It introduces two smooth metrics for vortices on black holes, revealing potential string splitting mechanisms and estimating pair production rates.

Findings

Vortex fields smooth out nodal singularities in idealized metrics.

Black hole pair production of strings is negligible at GUT scale.

Higher rates for macroscopic superstrings are possible but still very small.

Abstract

We construct two possible metrics for abelian Higgs vortices with ends on black holes. We show how the detail of the vortex fields smooths out the nodal singularities which exist in the idealized metrics. A corollary is that apparently topologically stable strings might be able to split by black hole pair production. We estimate the rate per unit length by reference to related Ernst and C-metric instantons, concluding that it is completely negligible for GUT-scale strings. The estimated rate for macroscopic superstrings is much higher, although still extremely small, unless there is an early phase of strong coupling.