Planetoid String Solutions in 3 + 1 Axisymmetric Spacetimes

TL;DR

This paper presents exact solutions for string propagation in axisymmetric spacetimes using a planetoid Ansatz, analyzes their behavior in Schwarzschild and de Sitter backgrounds, and explores their semiclassical quantization and Regge relations.

Contribution

It provides the first exact quadrature solutions for planetoid strings in axisymmetric spacetimes and examines their semiclassical quantization and spin/mass relations.

Findings

Strings stay outside the horizon in Schwarzschild spacetime.

In de Sitter spacetime, strings rotate around their center.

The Regge relation for these strings is non-linear.

Abstract

The string propagation equations in axisymmetric spacetimes are exactly solved by quadratures for a planetoid Ansatz. This is a straight non-oscillating string, radially disposed, which rotates uniformly around the symmetry axis of the spacetime. In Schwarzschild black holes, the string stays outside the horizon pointing towards the origin. In de Sitter spacetime the planetoid rotates around its center. We quantize semiclassically these solutions and analyze the spin/(mass$^2$) (Regge) relation for the planetoids, which turns out to be non-linear.