Scalar field perturbations of the Schwarzschild black hole in the Gödel universe

We investigate the scalar field perturbations of the 4+1-dimensional Schwarzschild black hole immersed in a G\"{o}del 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\"{o}del 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\"{o}del space-time against scalar field perturbations. The approximate analytical formula for large multipole numbers is found.Comment: 13 pages, 4 figures, 1 table, misprints corrected, to be published in Phys.Rev.