Mass and spin for classical strings in $dS_3$

TL;DR

This paper studies classical string solutions in de Sitter space, demonstrating they satisfy the Higuchi bound, analyzing their dynamics, and exploring implications for cosmic strings and horizon interactions.

Contribution

It extends the Higuchi bound to all rigidly rotating strings in dS_3 and analyzes their dynamics, including segmented strings and cosmic string interactions with horizons.

Findings

All rigidly rotating strings satisfy the Higuchi bound.

Strings violating the bound tend to expand towards the horizon.

Horizon friction can lengthen cosmic strings in dS space.

Abstract

We demonstrate that all rigidly rotating strings with center of mass at the origin of the $dS_3$ static patch satisfy the Higuchi bound. This extends the observation of Noumi et al. for the open GKP-like string to all solutions of the Larsen-Sanchez class. We argue that strings violating the bound end up expanding towards the horizon and provide a numerical example. Adding point masses to the open string only increases the mass/spin ratio. For segmented strings, we write the conserved quantities, invariant under Gubser's algebraic evolution equation, in terms of discrete lightcone coordinates describing kink collisions. Randomly generated strings are found to have a tendency to escape through the horizon that is mostly determined by their energy. For rapidly rotating segmented strings with mass/spin $<$ 1, the kink collisions eventually become causally disconnected. Finally we consider the scenario of cosmic strings captured by a black hole in dS and find that horizon friction can make the strings longer.