No-Go Theorem for Rotating Global Monopoles

TL;DR

This paper addresses whether rotating global monopoles can exist within Einstein gravity. It employs two independent lines of analysis: (i) a rigorous consistency check of rotating metrics generated by the Newman-Janis algorithm against the full Einstein-scalar field equations, which reveals an intrinsic theta-dependent inconsistency; and (ii) a comprehensive asymptotic analysis in the most general stationary, axisymmetric spacetime, which shows that any regular solution at infinity must be spherically symmetric. Collectively, these results establish a no-go theorem: nontrivial rotating global monopoles do not exist in general relativity, with the rotation function vanishing and the solution reducing to the static Barriola-Vilenkin monopole. This clarifies longstanding questions about rotating monopole spacetimes and sharpens predictions for their gravitational and lensing signatures.

Abstract

Global monopoles are topological defects predicted by certain grand unified theories and have been extensively studied for their astrophysical and cosmological implications, including their distinctive spacetime geometry and characteristic gravitational lensing effects. Despite this interest, an exact solution for a global monopole remains elusive, with research largely confined to approximations of the static, spherically symmetric case. This paper addresses the fundamental question of whether a rotating global monopole can exist as a solution to the coupled Einstein-scalar field equations. We first prove that metrics generated by applying the Newman-Janis algorithm to the static monopole are inconsistent with the scalar field's equation of motion. Furthermore, we perform an asymptotic analysis for general static, axially symmetric spacetimes and establish that the only such solution that is regular at large distances is the spherically symmetric one. These results lead to the definitive conclusion that non-trivial, rotating global monopole solutions are forbidden within the framework of Einstein's general relativity.