Classical Solutions of 2D String Theory in any Curved Spacetime

TL;DR

This paper constructs all classical solutions for 2D string theory in any curved spacetime, revealing complex behaviors near singularities like black holes and providing a comprehensive classification based on asymptotic conditions.

Contribution

It provides the first complete set of classical solutions for 2D string theory in arbitrary curved spacetimes, including a novel recursive mapping approach.

Findings

Solutions describe folded strings in curved spacetime

String behavior near singularities like black holes is analyzed

Solutions reduce to known folded string solutions in flat regions

Abstract

The complete set of solutions of two dimensional classical string theory are constructed for any curved spacetime. They describe folded strings moving in curved spacetime. Surprizing stringy behavior becomes evident at singularities such as black holes.The solutions are given in the form ofa map from the world sheet to target spacetime, where the world sheet has to be divided into lattice -like patches corresponding to different maps. A recursion relation analogous to a transfer matrix connects these maps into a single continuous map. This ``transfer matrix'' encodes the properties of the world sheet lattice as well as the geometry of spacetime. The solutions are completely classified by their behavior in the asymptotically flat region of spacetime where they reduce, as boundary conditions, to the folded string solutions that have been known for 19 years.