The global existence of smooth solutions of relativistic string equations in the Schwarzschild space-time

Details The global existence of smooth solutions of relativistic string equations in the Schwarzschild space-time The global existence of smooth solutions of relativistic string equations in the Schwarzschild space-time

2010-02-06

arxiv.org/abs/1002.1357v2

Mathematics

Analysis of PDEs

31 pages

Scientific paper

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.

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