Perturbations of spiky strings in flat spacetimes

TL;DR

This paper investigates the stability of spiky string solutions in flat spacetimes by analyzing small normal perturbations, showing that these perturbations lead to rounded spikes and demonstrate the solutions' stability.

Contribution

It provides exact solutions to the Jacobi equations for perturbations of spiky strings in flat spacetimes, revealing their stable nature and the effects of perturbations on spike profiles.

Findings

Finite normal perturbations cause spike rounding.

Spiky string stability is demonstrated through exact Jacobi solutions.

Results apply to both original and dual spiky string solutions in various dimensions.

Abstract

Perturbations of a class of semiclassical strings known today as spiky strings, are studied using the well-known Jacobi equations for small normal deformations of an embedded timelike surface. It is shown that there exists finite normal perturbations of the spiky string worldsheets embedded in a $2+1$ dimensional flat spacetime. Such perturbations lead to a rounding off of the spikes, which, in a way, demonstrates the stable nature of the unperturbed worldsheet. The same features appear for the dual spiky string solution and in the spiky as well as their dual solutions in $3+1$ dimensional flat spacetime. Our results are based on exact solutions of the corresponding Jacobi equations which we obtain and use while constructing the profiles of the perturbed configurations.