Reflections on the U(1) problem in general relativity

被引：0
作者：
Vincent Moncrief
机构：
[1] Yale University,Department of Physics
来源：
Journal of Fixed Point Theory and Applications | 2013年 / 14卷
关键词：
Primary 83C05; Secondary 35Q75; Einstein equations; Kaluza–Klein reduction; wave maps; Teichmüller space; Dirichlet energy; Bel–Robinson tensor; Hadamard descent; Hamiltonian reduction; Hadamard/Friedlander analysis; lightcone estimates;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
After reviewing the known stability results for vacuum, U(1) symmetric solutions to Einstein’s field equations, we shall describe some mathematical ideas and techniques that were unavailable during the earlier research in this area and which might conceivably be exploited to shed new light on the large data global Cauchy problem for this interesting class of spacetimes.
引用
收藏
页码：397 / 418
页数：21
相关论文
共 35 条
[1]  
Andersson L.(2005)Constant mean curvature foliations of simplicial flat spacetimes Comm. Anal. Geom. 13 963-979
[2]  
Andersson L.(2003)Elliptic-hyperbolic systems and the Einstein equations Ann. Henri Poincaré 4 1-34
[3]  
Moncrief V.(2011)Einstein spaces as attractors for the Einstein flow J. Differential Geom. 89 1-47
[4]  
Andersson L.(2003)Feuilletages des espaces temps globalement hyperboliques par des hypersurfaces à courbure moyenne constante C. R. Math. Acad. Sci. Paris 336 245-250
[5]  
Moncrief V.(2001)Cosmological time in (2+1)-gravity Nuclear Phys. B 613 330-352
[6]  
Barbot T.(1991)Yang-Mills-Higgs fields in three space time dimensions Mém. Soc. Math. France (N.S.) 46 73-97
[7]  
Béguin F.(1994)An existence theorem for the reduced Einstein equations C. R. Acad. Sci. Paris Sér. I Math. 319 153-159
[8]  
Zeghib A.(2001)Future global-in-time Einsteinian spacetimes with U(1) Ann. Henri Poincaré 2 1007-1064
[9]  
Benedetti R.(1997)Solutions of the Yang-Mills equations on globally hyperbolic four-dimensional Lorentzian manifolds Asian J. Math. 1 530-548
[10]  
Guadagnini E.(1982)The global existence of Yang-Mills-Higgs fields in 4-dimensional Minkowski space. II. Completion of proof Comm. Math. Phys. 83 193-212
1234