Thickening the string. I. The string perfect dust

Abstract

The classical theory of the geometrical string is developed as the theory of a simple, surface-forming timelike bivector field in an arbitrary background space-time. The stress-energy tensor for a perfect dust of such strings is written down, and the conservation laws for such a dust, as well as the equations of motion of the string, are derived from the vanishing of the divergence of the stress-energy tensor. (The boundary conditions for the open string are also derived from the junction conditions for the stress-energy tensor in Appendix A.) The generalization of this model to null strings, and to a perfect fluid of strings, are discussed, and will form the subject of the second and third papers in this series. The problem of a fully general-relativistic string theory, and an alternate approach to the string, based upon defining an acceleration tensor for two- (and higher) dimensional subspaces, are also discussed.