Strings in Homogeneous Background Spacetimes

TL;DR

This paper derives and solves string equations of motion in homogeneous cosmological spacetimes, exploring solutions for tensile and null strings, with implications for string cosmology and string-vacua.

Contribution

It provides explicit solutions for string equations in specific homogeneous backgrounds, including null and tensile strings, advancing understanding in string cosmology.

Findings

Explicit solutions for string equations in Kantowski-Sachs, Bianchi I, Bianchi IX spacetimes.

Null strings simplify to geodesic equations with additional constraints.

Discussion of circular and elliptic string ansatz in homogeneous backgrounds.

Abstract

The string equations of motion for some homogeneous (Kantowski-Sachs, Bianchi I and Bianchi IX) background spacetimes are given, and solved explicitly in some simple cases. This is motivated by the recent developments in string cosmology, where it has been shown that, under certain circumstances, such spacetimes appear as string-vacua. Both tensile and null strings are considered. Generally, it is much simpler to solve for the null strings since then we deal with the null geodesic equations of General Relativity plus some additional constraints. We consider in detail an ansatz corresponding to circular strings, and we discuss the possibility of using an elliptic-shape string ansatz in the case of homogeneous (but anisotropic) backgrounds.