MG15 - Talk detail

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We investigate rigidly rotating Nambu-Goto strings in a Kerr spacetime. Since such a string world sheet admits a Killing vector, the Nambu-Goto equation of the rigidly rotating string reduces to the geodesic equation on the orbit space defined by the action of isometries generated by the Killing vector. By the analysis of the geodesic equation, we found the following two facts. The first is that the rigidly rotating strings can be trapped in a finite region around the black hole. As a snapshot of the string, chaotic behavior appears in the configuration. The second is that the rigidly rotating string can stick into the horizon only if the energy and angular momentum flows on the sticking string satisfy the 2nd law of the black hole thermodynamics on the horizon. Then, only one end of the string is possible to stick.

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We show numerically the existence of non-topological soliton solutions in the system that consists of a massless complex scalar field coupled with a U(1) gauge field, and a complex Higgs scalar field with the Mexican hat potential which causes the spontaneous symmetry breaking. This system is a generalization of the Friedberg-Lee-Sirlin (FLS) model. The non-topological solitons obtained in this work are stationary and spherically symmetric localized solutions of the system. In the asymptotic far region, the U(1) symmetry is broken by the vacuum expectation value of the Higgs field, while in the central region, the massless scalar field yields charge distribution by its phase rotation. Immediately, the Higgs field and the gauge field yield counter charge which shield the source charge. Therefore, the all fields are localized in a finite region of the space. Implications of the solutions are discussed.

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