Nonlinear Dynamics Of Relativistic String With The Physical Space-time Relativity Film

The thesis concerns with the dynamics of relativistic strings moving on the equatorial plane in the Schwarzschild space-time and relativistic membranes in the Schwarzschild-anti de Sitter space-time. It is organized as follows.Chapter1briefly recalls the present situation of the study on the motion of relativistic string and relativistic membrane in several space-times. The central problems under consideration and the main results obtained are stated.Chapter2concentrates on the dynamics of relativistic string moving on the equatorial plane in the Schwarzschild space-time. By variational method, the equation for the relativistic string moving on the equatorial plane in the Schwarzschild space-time is derived, which is a nonlinear wave equation. Based on this, we discuss a special situation, that is, r is only depend on t. First, we re-call the basic equations for the motion of relativistic strings in the Schwarzschild space-time and present the equation of motion on the equatorial plane. Next we study systematically on the solutions of the equations for the motion of rela-tivistic closed strings on the equatorial plane. At the same time, some new and interesting physical phenomena is discovered and illustrated:the motion with different initial velocity has essentially different behavior.In Chapter3, we discuss the dynamics of relativistic membrane in the Schwarzschild-anti de Sitter space-time. Similarly, by variational method, we ob-tain the basic equation for the motion of relativistic membrane in the Schwarzschild-anti de Sitter space-time. Then we study systematically on the spherical sym-metric solutions of the equations for the motion of relativistic membranes. By discussion, some new and interesting physical phenomena is discovered:motion of the spherical membrane may be different due to the relationship between critical velocity and initial velocity.