Magnetic monopole meets primordial black hole: an extended analysis

TL;DR

This paper analytically demonstrates that primordial black holes cannot significantly reduce magnetic monopole abundance through gravitational capture during radiation domination, thus not solving the monopole problem.

Contribution

It provides a rigorous analytical proof that PBH capture cannot lower monopole abundance in a radiation-dominated early universe, clarifying previous assumptions.

Findings

PBH capture does not reduce monopole abundance below initial levels

Analytical proof applies to all extended PBH mass functions in radiation era

Monopole problem remains unresolved by PBH capture in early universe

Abstract

We investigate gravitational capture of magnetic monopoles by primordial black holes (PBH) that evaporate before Big Bang Nucleosynthesis (BBN), a hypothetical process which was once proposed as an alternative solution to the monopole problem. Magnetic monopoles produced in phase transitions of a grand or partially unified gauge theory are considered. We prove analytically that for all extended PBH mass functions that preserve radiation domination, it is impossible to reduce the monopole abundance via gravitational capture by PBHs to values significantly below the one set by monopole annihilation (or below its initial abundance if it is smaller), regardless of the nature of the capture process (diffusive or non-diffusive). Therefore, the monopole problem cannot be solved by PBH capture in a radiation-dominated era in the early universe.