The sine-Gordon equation and its application to black holes

Abstract

Linear and nonlinear wave equations are important in various aspects of mathematics and physics, including the study of black holes. After a brief survey of the sine-Gordon equation (SGE), this report presents a fourth-order numerical approximation scheme for solving equations of this type. This is followed by a numerical investigation of SGE in the presence of the PoschlTeller potential. We close with a discussion of the application of this method to the study of black hole dynamics.