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Regular stationary solutions of the cylindrically symmetric Einstein-matter-gauge equations. (English) Zbl 0858.53068

The paper establishes the existence of regular stationary solutions of the coupled Einstein-matter-gauge equations with cylindrical symmetry. Such solutions are called cosmic strings or gravitational vortices and are believed to have important implications in cosmology and quantum physics. It is shown that for a prescribed string location with a string or winding number below an explicit barrier, the system possesses a continuous family of distinct finite-energy solution configurations. The proof of the main existence theorem relies on a special shooting method.

MSC:

53Z05 Applications of differential geometry to physics
83C22 Einstein-Maxwell equations
35Q75 PDEs in connection with relativity and gravitational theory
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