Membranes with a symmetry of cohomogeneity one

Abstract

We study the dynamics of the Nambu-Goto membranes with cohomogeneity one symmetry, i.e., the membranes whose trajectories are foliated by homogeneous surfaces. It is shown that the equation of motion reduces to a geodesic equation on a certain manifold, which is constructed from the original spacetime and Killing vector fields thereon. A general method is presented for classifying the symmetry of cohomogeneity one membranes in a given spacetime. The classification is completely carried out in Minkowski spacetime. We analyze one of the obtained classes in depth and derive an exact solution.

References in corpus (2)

• Stationary strings and branes in the higher-dimensional Kerr-NUT-(A)dS spacetimes
• Stationary Rotating Strings as Relativistic Particle Mechanics

Cited by in corpus (1)

• Self-similar motion of a Nambu-Goto string