GRAVITATING (BI-)SPHALERONS

Abstract

The standard model of electroweak interactions is minimally coupled to gravity and the response of the spherically symmetric solutions — the sphaleron and the bisphaleron — to gravity is emphasized. For a given value of the Higgs mass M H, several branches of solutions exist which terminate into cusp-catastrophy at some ( M H-depending) critical value of the parameter α defined by the ratio of the vector–boson mass to the Planck mass. A given branch either bifurcates from another at an intermediate value of α or persists in the limit α→0 where it terminates into a flat sphaleron or bisphaleron or into a Bartnik–McKinnon solution. These bifurcation patterns are studied in some details.