The (in)stability of global monopoles revisited

Abstract

We analyse the stability of global O(3) monopoles in the infinite cut-off (or scalar mass) limit. We obtain the perturbation equations and prove that the spherically symmetric solution is classically stable (or neutrally stable) to axially symmetric square integrable or power-law decay perturbations. Moreover we show that, in spite of the existence of a conserved topological charge, the energy barrier between the monopole and the vacuum is finite even in the limit where the cut-off is taken to infinity. This feature is specific of global monopoles and independent of the details of the scalar potential.

Comments: 6 pages, 2 figures (uses RevTeX and epsf). Corrected an error in the original proof of stability, discussion extended to non-normalizable perturbations, one figure slightly modified, minor changes