Membranes with a symmetry of cohomogeneity one

TL;DR

This paper investigates cohomogeneity one symmetric membranes in spacetime, reducing their dynamics to geodesic equations, classifies their symmetries in Minkowski space, and provides an exact solution for a specific class.

Contribution

It introduces a general method for classifying cohomogeneity one membranes and applies it comprehensively to Minkowski spacetime, deriving explicit solutions.

Findings

Reduction of membrane equations to geodesic equations

Complete classification of cohomogeneity one membranes in Minkowski space

Derivation of an exact solution for a specific class

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.