Nambu-Goto strings with a null symmetry and contact structure

We study the classical dynamics of the Nambu-Goto strings with a null symmetry in curved spacetimes admitting a null Killing vector field. The Nambu-Goto equation is reduced to first-order ordinary differential equations and is always integrable in contrast to the case of non-null symmetries where integrability requires additional spacetime symmetries. It is found that in the case of null symmetry, an almost contact structure associated with the metric dual 1-form eta of the null Killing vector field emerges naturally. This structure determines the allowed class of string worldsheets in such a way that the tangent vector fields of the worldsheet lie in ker d eta. In the special case that the almost contact structure becomes a contact structure, its Reeb vector field completely characterizes the worldsheet. We apply our formulation to the strings in the pp-waves, the Einstein static universe and the Godel universe. We also study their worldsheet geometry in detail.

Automated summary

We study the classical dynamics of Nambu-Goto strings with null symmetry in curved spacetimes. In the case of null symmetry, an almost contact structure associated with the metric dual 1-form eta of the null Killing vector field emerges naturally and determines the allowed class of string worldsheets.