Classical String in Curved Backgrounds

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.

12 pages, REVTeX 4. Added a note and one reference

References in corpus (3)

• An Einstein-Hilbert Action for Axi-Dilaton Gravity in 4-Dimensions
• Bosonic string theory in background fields by canonical methods
• CT-duality as a local property of the world-sheet

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• Test membranes in Riemann-Cartan spacetimes
• String background fields and Riemann-Cartan geometry
• Single-Pole Interaction of the Particle with the String
• Interaction of the Particle with the String in Pole-Dipole Approximation