Abstract
This paper concerns motion of relativistic membranes in the Schwarzschild-anti de Sitter space-time. We derive a nonlinear equation for relativistic membranes moving in the Schwarzschild-anti de Sitter space-time, discuss spherical symmetric solutions for the motion equations, and obtain some interesting physical results.
Highlights
This paper concerns the motion of relativistic strings in the Schwarzschild-anti de Sitter space-time
The Schwarzschild-anti de Sitter space-time is a fundamental physical space-time; it plays an important role in general relativity, the theory of black holes, and modern cosmology
This paper mainly focuses on the equations and spherical symmetric solutions for the motion of relativistic membranes in the Schwarzschild-anti de Sitter space-time
Summary
This paper concerns the motion of relativistic strings in the Schwarzschild-anti de Sitter space-time. In [15], Kong et al investigated the dynamics of relativistic strings in the Minkowski spacetime R1+n (n ≥ 2) They first obtained a system with n nonlinear wave equations of Born-Infeld type describing the motion of the string, and they showed that this system enjoyed some interesting geometric properties; in the end, they gave a sufficient and necessary condition for the global existence of extremal surfaces without a space-like point in R1+n. They made a lot of numerical analyses demonstrating that various topological singularities developed in finite time in the motion of the string.
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