Systematic method for solving strings having a symmetry in the space-time
Tatsuhiko Koike · 2009
In the presence of certain symmetry, called cohomogeneity-one symmetry, the equation of motion of an extended object in spacetime reduces to the problem of finding geodesics on a certain orbit space.We present a general method for obtaining solutions of such extented objects and classifying them.The classification is carried out in 4-dimensional Minkowski space and in 5dimensional anti-de Sitter space.The solvability condition is described in terms of Killing vectors and Killing tensors which mutually commute.In 4-dimensional Minkowski space, it is found that all types of cohomogeneity-one strings are solvable.In the case of 5-dimensional de Sitter space, there are not enough number of commuting Killing vectors but that the problem reduces to that of finding curves on a two-dimensional surface. Black Holes in General Relativity and String Theory 24-30