2020/10/01 by Chengjian Yao, Yao, Chengjian
Mathematics · Physics and Astronomy · #53C07(Primary) #53C25(Secondary) #Black Holes and Theoretical Physics #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2010.00264
openalex publication_date 2020/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the notion of twisted gravitating vortex on a compact Riemann surface. If the genus of the Riemann surface is greater than 1 and the twisting forms have suitable signs, we prove an existence and uniqueness result for suitable range of the coupling constant generalizing the result of arXiv:1510.03810v2 in the non twisted setting. It is proved via solving a continuity path deforming the coupling constant from 0 for which the system decouples as twisted Kähler-Einstein metric and twisted vortices. Moreover, specializing to a family of twisting forms smoothing delta distribution terms, we prove the existence of singular gravitating vortices whose Kähler metric has conical singularities and Hermitian metric has parabolic singularities. In the Bogomol'nyi phase, we establish an existence result for singular Einstein-Bogomol'nyi equations, which represents cosmic strings with singularities.