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ZhETF, Vol. 148, No. 6, p. 1130 (December 2015)
(English translation - JETP, Vol. 121, No. 6, p. 991, December 2015 available online at )

Shnir Ya.M.

Received: May 30, 2015

DOI: 10.7868/S0044451015120081

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We construct solutions of the 3+1 dimensional Faddeev-Skyrme model coupled to Einstein gravity. The solutions are static and asymptotically flat. They are characterized by a topological Hopf number. We investigate the dependence of the ADM masses of gravitating Hopfions on the gravitational coupling. When gravity is coupled to flat space solutions, a branch of gravitating Hopfion solutions arises and merges at a maximal value of the coupling constant with a second branch of solutions. This upper branch has no flat space limit. Instead, in the limit of a vanishing coupling constant, it connects to either the Bartnik-McKinnon or a generalized Bartnik-McKinnon solution. We further find that in the strong-coupling limit, there is no difference between the gravitating solitons of the Skyrme model and the Faddeev-Skyrme model.

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