We investigate the instability of charged massive scalar fields in Kerr-Newman spacetime. Due to the super-radiant effect of the background geometry, the bound state of the scalar field is unstable, and its amplitude grows in time. By solving the Klein-Gordon equation of the scalar field as an eigenvalue problem, we numerically obtain the growth rate of the amplitude of the scalar field. Although the dependence of the scalar field mass and the scalar field charge on this growth rate agrees with the result of the analytic approximation, the maximum value of the growth rate is three times larger than that of the analytic approximation. We also discuss the effect of the electric charge on the instability of the scalar field. * )

A numerical simulation of fluid flows in a Laval nozzle is performed to observe the formation of an acoustic black hole and the classical counterpart to Hawking radiation under a realistic setting of the laboratory experiment. We aim to construct a practical procedure of the data analysis to extract the classical counterpart to Hawking radiation from experimental data. Following our procedure, we determine the surface gravity of the acoustic black hole from obtained numerical data.Some noteworthy points in analyzing the experimental data are clarified through our numerical simulation.