Instability of stationary closed strings winding around flat torus in five-dimensional Schwarzschild spacetimes

TL;DR

This paper analyzes the stability of stationary closed strings in five-dimensional Schwarzschild spacetime, showing they are always unstable regardless of their position, with solutions expressed through elementary operations.

Contribution

It provides a solvable framework for linear perturbations of closed strings in higher-dimensional black hole backgrounds and proves their universal instability.

Findings

Strings are always unstable regardless of location.

Perturbation modes are explicitly solvable using elementary operations.

Frequency spectra are expressed with radicals and arithmetic operations.

Abstract

Linear perturbations for a one parameter family of stationary, closed Nambu-Goto strings winding around a flat torus in the five-dimensional Schwarzschild spacetime have been studied. It has been shown that this problem is solvable in the sense that frequency spectra and perturbation modes can be expressed only with arithmetic operations and radicals. It has been proven that the Nambu-Goto strings belonging to this family are always unstable, no matter how they are located at almost flat region distant from the event horizon.