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- W2329121460 abstract "In the context of static cosmic strings, the Einstein equations coupled to the Abelian Higgs model and the gauged σ-model reduce into a single equation, which directly relates the Gauss curvature of a Riemann surface hosting nontrivial geometry and gravitation to the energy density of the coupled matter-gauge sector. This equation gives rise to an equivalence relation between the topology of the Riemann surface and the topology of the complex line bundle which hosts and is determined by the physical interactions of the matter-gauge sector. The existence of solutions realizing a prescribed distribution of cosmic strings resembles the classical prescribed Gauss curvature problem. 1. Geometry, Physics, and Governing Equations Geometry, Physics, and the Einstein Equations. The basic principle that led Einstein to write down his fundamental equations for gravitation is that the geometry of spacetime which governs the gravitation in it is determined by the matter it contains. These equations may be viewed as the equations of motion of Received December 9, 2005. ∗This survey article is written based on a talk given at the conference Partial Differential Equations and Calculus of Variations in honor of Professors Robert Gulliver, Robert Hardt, and Leon Simon on the occasion of their 60th birthdays, Zhejiang University, Hangzhou, China, June 23–28, 2005." @default.
- W2329121460 created "2016-06-24" @default.
- W2329121460 creator A5065159121 @default.
- W2329121460 date "2007-01-01" @default.
- W2329121460 modified "2023-10-17" @default.
- W2329121460 title "Geometry, Topology, and Gravitation Synthesized by Cosmic Strings" @default.
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- W2329121460 doi "https://doi.org/10.4310/pamq.2007.v3.n3.a4" @default.
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