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Gravitating (bi-)sphalerons

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 one at an intermediate value of $α$ or persists in the limit $α\to 0$ where it terminates into a flat sphaleron or bisphaleron or into a Bartnik-McKinnon solution. These bifurcation patterns are studied in some details.