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.

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Cited by in corpus (6)

• Black holes, hidden symmetries, and complete integrability
• Rigidly Rotating String Sticking in a Kerr Black Hole
• Scale invariance and constants of motion
• Self-similar motion of a Nambu-Goto string
• Note on orbit space of G membranes
• Instability of stationary closed strings winding around flat torus in five-dimensional Schwarzschild spacetimes