2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/109878Carefully analyze influence of the tortoise coordinates r* and t on the stable study of the Schwarzschild black hole. Actually, one should be cautious in using the compact property of the perturbation field: it is true only with respect with the coordinate r and proper time or "good time", not the tortoise coordinates r* and t. Therefore, the mathematical proof used in reference [7] is incorrect because of it relying on the compact property of the perturbation fields. The Schwarzschild black hole might be unstable[1]-[5]5pages, no figureGeneral Relativity and Quantum Cosmologytext