2010/02/06 by Chun-Lei He, He, Chun-Lei, De-Xing Kong +1
Mathematics · #35L70 #35Q75 #70H40 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35L70 #msc:35Q75 #msc:70H40
paper · pdf · doi:10.48550/arxiv.1002.1357
31 pages
arxiv created 2010/02/09 · arxiv updated 2010/02/26
This paper concerns the motion of relativistic strings in the Schwarzschild space-time. As a general framework, we first analyze the basic equations for the motion of a p-dimensional extended object in a general enveloping space-time (N; ~g), which is a given Lorentzian manifold, and then particularly investigate the interesting properties enjoyed by the equations for the motion of relativistic strings in the Schwarzschild space-time. Based on this, under suitable assumptions we prove the global existence of smooth solutions of the Cauchy problem for the equations for the motion of relativistic strings with small arc length in the Schwarzschild space-time.