Barriola-Vilenkin global monopoles are incompatible with rotation in Einstein gravity because rotating metrics fail the scalar equation of motion and asymptotic regularity forces spherical symmetry.
Erbin,Janis–Newman Algorithm: Generating Rotat- ing and NUT Charged Black Holes, Universe3, 19 (2017)
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Why Barriola--Vilenkin Global Monopoles Cannot Rotate?
Barriola-Vilenkin global monopoles are incompatible with rotation in Einstein gravity because rotating metrics fail the scalar equation of motion and asymptotic regularity forces spherical symmetry.