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

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