Classical String in Curved Backgrounds

TL;DR

This paper extends the Mathisson-Papapetrou method to derive equations of motion and boundary conditions for extended objects like strings in curved backgrounds, revealing more general world sheet equations dependent on internal structure.

Contribution

It generalizes the Mathisson-Papapetrou approach to strings, deriving new equations that incorporate internal structure and classifying different physical and unphysical string cases.

Findings

Derived generalized string equations of motion and boundary conditions.

Classified string types based on stress-energy tensor forms.

Connected specific cases to known models like Nambu-Goto strings.

Abstract

The Mathisson-Papapetrou method is originally used for derivation of the particle world line equation from the covariant conservation of its stress-energy tensor. We generalize this method to extended objects, such as a string. Without specifying the type of matter the string is made of, we obtain both the equations of motion and boundary conditions of the string. The world sheet equations turn out to be more general than the familiar minimal surface equations. In particular, they depend on the internal structure of the string. The relevant cases are classified by examining canonical forms of the effective 2-dimensional stress-energy tensor. The case of homogeneously distributed matter with the tension that equals its mass density is shown to define the familiar Nambu-Goto dynamics. The other three cases include physically relevant massive and massless strings, and unphysical tahyonic strings.