Circular String-Instabilities in Curved Spacetime

TL;DR

This paper studies how curved spacetime backgrounds like Schwarzschild, Reissner-Nordström, and de Sitter influence string instabilities, revealing growth of perturbations near singularities and at infinity, confirming previous findings.

Contribution

It extends the analysis of string instabilities to various curved spacetimes, providing detailed linear perturbation results in these backgrounds.

Findings

Radial perturbations grow infinitely as r approaches 0 in all three spacetimes.

Angular perturbations are bounded near r=0.

Perturbations blow up at infinity in de Sitter space.

Abstract

We investigate the connection between curved spacetime and the emergence of string-instabilities, following the approach developed by Loust\'{o} and S\'{a}nchez for de Sitter and black hole spacetimes. We analyse the linearised equations determining the comoving physical (transverse) perturbations on circular strings embedded in Schwarzschild, Reissner-Nordstr\"{o}m and de Sitter backgrounds. In all 3 cases we find that the "radial" perturbations grow infinitely for $r\rightarrow 0$ (ring-collapse), while the "angular" perturbations are bounded in this limit. For $r\rightarrow\infty$ we find that the perturbations in both physical directions (perpendicular to the string world-sheet in 4 dimensions) blow up in the case of de Sitter space. This confirms results recently obtained by Loust\'{o} and S\'{a}nchez who considered perturbations around the string center of mass.