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We investigate the scalar field perturbations of the 4+1-dimensional Schwarzschild black hole immersed in a G\"odel universe, described by the Gimon-Hashimoto solution. This may model the influence of the possible rotation of the universe upon the radiative processes near a black hole. In the regime when the scale parameter j of the G\"odel background is small, the oscillation frequency is linearly decreasing with j, while the damping time is increasing. The quasinormal modes are damping, implying stability of the Schwarzschild-G\"odel space-time against scalar field perturbations. The approximate analytical formula for large multipole numbers is found.
Konoplya et al. (Fri,) studied this question.